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Carr G.S. — Formulas and Theorems in Pure Mathematics

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Название: Formulas and Theorems in Pure Mathematics

Автор: Carr G.S.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1970

Количество страниц: 988

Добавлена в каталог: 07.05.2008

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Предметный указатель

Indeterminate equations, quartic      geo.cnL.63
Indeterminate equations, quintic      J.3
Indeterminate equations, simultaneous, $x+y+z=\cap$ ; $x^{2}+y^{2}+z^{2}=\cap$ ; $x^{3}+y^{3}+z^{3}=\cap$       E.17
Indeterminate equations, simultaneous, $x=u^{2}$ ; $x+1=2v^{2}$ ; $2x+1=3w^{2}$       N.78
Indeterminate equations, simultaneous, $x^{2}+a=y^{2}$ ; $y^{2}-a=z^{2}$       An.55 C.78
Indeterminate equations, simultaneous, $x^{2}+axy+y^{2}=\cap$ ; $y^{2}+ayz+z^{2}=\cap$ ; $z^{2}+azx+x^{2}=\cap$       E.20 21
Indeterminate equations, simultaneous, $x^{2}+x+2=y^{2}$ ; $x^{2}-x-2=z^{2}$       N.76
Indeterminate equations, simultaneous, $x^{2}+y^{2}-z^{2}=\cap$ ; $x^{2}-y^{2}+z^{2}=\cap$ ; $-x^{2}+y^{2}+z^{2}=\cap$       E.20
Indeterminate equations, simultaneous, ax+by+cz=0; Ayz+Bzx+Cxy=0      A.28
Indeterminate equations, simultaneous, six eqs. in nine unknowns      N.50
Indeterminate forms      1580—1593 A.26 AJ.1
Indeterminate forms with two variables      1592a
Indeterminate forms, exponential      J.1 Me.75 N.48 77
Indeterminate forms, exponential, $\frac{0}{0}$       A.21 Z.1
Indeterminate forms, exponential, $\frac{f(x)}{x}$ when $x=\infty$       1592
Indeterminate forms, exponential, $\frac{f(x)}{x}$ when $x=\infty$ , $0^{0}$       J.11 12
Indeterminate forms, exponential, $\frac{f(x)}{x}$ when $x=\infty$ , $0^{0}$ , $0 exp 0^{x}$       J.6
Indeterminate forms, exponential, $\frac{\infty}{\infty}$       L.41 42 N.46
Indeterminate multipliers      213 1862 3346 N.47
Index law      1490
Indian arithmetic, th      L.57
Indian arithmetic, th, calculation of sines      N.54
Indicatrix      5795 C.92 Me.72 N.74
Indicatrix, a rect. hyperbola, condition      5824
Indicatrix, an umbilicus      5819
Indicatrix, determination of a surface from the indicatrix      A.59
Indicatrix, to determine its axes      L.78 82
Indicatrix, two coinciding lines      5825
indices      29 N.76 77 78
Indices in relation to conics      N.72
Indices of functions, calculus of      JP.15
Induction      233 C.39 G.15 L.48
Inequalities      330—341 A.1 24
Inequalities in integrals      Mel.3 f.d.c.Mem.59
Inequalities in integrals, $(\underline{|n})^{2}>n^{n}$       N.60
Inequalities, $a^{x}>x$       A.14
Inequalities, geo. mean of n numbers < arith. mean      332 N.42
Inequalities, if $x^{2}+y^{2}=z^{2}$ , $x^{m}+y^{m}{> \atop <}z^{m}$       A.20
Infinite equalities      M.10 prG.22
Infinite from gnomonic projection      Me.66
Infinite functions      An.71 J.54
Infinite linear point-manifoldness      M.15 17 20 21 23
Infinite point-mass      M.23
Infinite products      J.27 N.69
Infinite products, exhibiting circular arcs, logarithms and elliptic functions of the 1st kind      J.73 Ac.4
Infinite products, value expressed by $\Gamma$ functions      Ac.3
Infinite, use of in mathematics      C.73
Infinitesimal calculus      1407 M.11 18
Infinitesimal geometry      An.59 C.82
Infinitesimal geometry of a surface, formulae      G.13
Infinity, points at on alg. surfaces      C.59
Inflexion curves      Z.10
Inflexion points      5175 CM.4 J.41
Inflexion points of cubic curves      J.28
Inflexion points of cubic curves, axis      E.31
Inflexion points, Herse's equation      N.81
Inflexional tangents      5789 A.35
Inflexional tangents of a cubic curve      E.30 J.38 58
Inscribed figures and circum-circles of a polygon      N.45
Inscribed figures and circum-circles of a polygon, distance of centres      A.32
Inscribed figures and circum-circles of a quadrilateral      Fuss's prMel.3
Inscribed figures and circum-circles of a triangle      935 A.38
Inscribed figures and circum-circles of a triangle, distance of centres      936 4972
Inscribed figures and circum-circles of a triangle, distance of centres, eq      4644
Inscribed figures and circum-conics of a pentagon      N.78
Inscribed figures and circum-conics of a polygon      J.64 70
Inscribed figures and circum-conics of a polygon, regular      Z.14
Inscribed figures and circum-conics of a quadrilateral: 60 theorems      N.45 N.76
Inscribed figures and circum-conics of a self-conjugate triangle      Me.81
Inscribed figures and circum-conics of a triangle      4724 4739 An.52 G.22
Inscribed figures and circum-heptagons of a conic      A.3
Inscribed figures and circum-pentagon of a circle      A.22 43
Inscribed figures and circum-polygons of a circle      L.16 N.80 P.11 Q.11 see
Inscribed figures and circum-polygons of a circle, difference of perimeters, ths      N.43
Inscribed figures and circum-polygons of a circle, sum of squares of perps., &c.      ths1099
Inscribed figures and circum-polygons of a conic      A.4
Inscribed figures and circum-polygons of a conic, ellipse      An.52 An.57 J.64 N.57 84
Inscribed figures and circum-polygons of a curve      C.78
Inscribed figures and circum-polygons of a homonymous polygon      A.50
Inscribed figures and circum-polygons of two circles, respectively      C.53 G.21 L.78
Inscribed figures and circum-polygons of two conics      C.90
Inscribed figures and circum-quadrics of a tetrahedron      eqsN.65
Inscribed figures and circum-quadrilaterals of a circle      A.48
Inscribed figures and circum-quadrilaterals of a conic      4709
Inscribed figures and circum-quadrilaterals of a conic and pentagon ths      N.48
Inscribed figures and circum-spheres of a regular polygon      A.32
Inscribed figures and circum-spheres of a regular polyhedron      910
Inscribed figures and circum-spheres of a tetrahedron      N.73
Inscribed figures and circum-triangles and square of an ellipse      A.30
Inscribed figures and circum-triangles of a circle (Castillon's pr)      Q.3
Inscribed figures and circum-triangles of two conics      4970 N.80
Inscribed figures and circum-triangles of two conics, envelope of base      4997
Inscribed figures and circum-triangles, equilateral, of another triangle      Me.74
Inscribed figures and circum-triangles, respectively of two conics having a common pole and axis      CD.4
Inscribed figures, circle of a quadrilateral, locus of centre      A.52
Inscribed figures, circle of a triangle      709 953 4747—4750 tg.e4889 CM.1
Inscribed figures, circle of a triangle, inscribed centre      709 t.c tg.e4882
Inscribed figures, conic of a circle      thJ.91
Inscribed figures, conic of a developable quartic      An.59
Inscribed figures, conic of a polygon      M.25
Inscribed figures, conic of a quadric      J.41
Inscribed figures, conic of a quadrilateral      tg.e4907 N.63
Inscribed figures, conic of a quadrilateral, four      N.56
Inscribed figures, conic of a triangle      4739—4746 tg.e4887 A.2 N.50
Inscribed figures, conic of a triangle, max      A.8 Q.2
Inscribed figures, conic of a triangle, max, lat. rect.      E.34
Inscribed figures, conic, four of a conic      prJ.39
Inscribed figures, cubic of a pencil of six lines      Q.9
Inscribed figures, hexagon of a circle      A.22
Inscribed figures, hexagon of a conic      4781 N.57 82
Inscribed figures, parabola of a triangle      CD.7
Inscribed figures, pentahedron of a cubic      Ac.5 M.5
Inscribed figures, polygons of a circle      746 CM.1 J.35 N.50
Inscribed figures, polygons of a circle and conic (Poncelet)      G.1
Inscribed figures, polygons of a circle, do. 17 sides      TI.13
Inscribed figures, polygons of a circle, do. 5, 6, 10 sides, relation      A.40 43 45 48
Inscribed figures, polygons of a circle, do. 9 and 11 sides      LM.10
Inscribed figures, polygons of a circle, do. four of 30 sides      N.78
Inscribed figures, polygons of a circle, regular of 15, 30, 60, 120, &c., sides      A.62
Inscribed figures, polygons of a circle, two stars, one double the other      A.61
Inscribed figures, polygons of a conic      4822 thsN.47 cnTN.69
Inscribed figures, polygons of a conic, semi-regular      N.63
Inscribed figures, polygons of a conic, with sides through given points, cn      4823 An.51
Inscribed figures, polygons of a cubic (Steiner)      M.24
Inscribed figures, polygons of a curve      Q.7
Inscribed figures, polygons of a polygon, th      CD.5
Inscribed figures, polygons of a quadric with sides through given points      LM.2
Inscribed figures, quadrics of a developable      Q.10
Inscribed figures, quadrics of a developable, quartic      An.59
Inscribed figures, quadrics, 6 of a quadric, 2 touching 4      An.69
Inscribed figures, quadrilateral of a circle      733 A.5 cnE.21
Inscribed figures, quadrilateral of a circle, area      N.44 P.14
Inscribed figures, quadrilateral of a conic      4709
Inscribed figures, quadrilateral of a cubic      N.84
Inscribed figures, sphere of a tetrahedron      A.61
Inscribed figures, spherical quadrilateral      N.49
Inscribed figures, square of a circle      J.32
Inscribed figures, square of a quadrilateral      A.6
Inscribed figures, triangles of a circle      P.71
Inscribed figures, triangles of a circle with sides through given points      J.45 N.44
Inscribed figures, triangles of a conic      J.7
Inscribed figures, triangles of a conic of a triangle      thsQ.21
Inscribed figures, triangles of a conic with given centroid      G.23
Inscribed figures, triangles of a conic, Maccullagh's th      N.65
Inscribed figures, triangles of a conic, similar      A.9
Inscribed figures, triangles of a conic, two (Steiner's "Gegenpunkte")      J.62
Instantaneous centre      5243
Integrability of functions      An.50 73 C.28 J.59 79 JP.17 L.49
Integrability of functions, criterion for max. and min. values of a primitive      An.52
Integral calculus      1900—2997 A.ext18 26

Integral calculus, Euler's      A.20 C.14 42
Integral calculus, Newton      CD.8 G.19 L.47 Me.72 74 75 Mem.18 36
Integral calculus, paradoxes      C.44
Integral calculus, theorems, &c.      2700—2742 A.45 C.13 L.geo.ap50 56 Me.77 Mem.prs15 30
Integral functions      C.88 89 98 G.4 22
Integral functions and continued fractions      An.77
Integral functions with binomial divisors      J.70
Integral functions, h.c.f of      G.2
Integral functions, reciprocal relation of      A.67
Integrals or Integration      1908 A.1 2 4 5 6 10 23 Ac.1 32 44 C.90 CD.9 CP.3 J.2 4 8 17 25 36 39 61 92 JP.9 10 11 L.39 M.6 16 73 75 Mem.31 P.14 36 37 Pr.7 39 Q.11 13 Z.7 11 15 18 22 23
Integrals or Integration and gamma-function      LM.12 Z.9 12
Integrals or Integration and Taylor's theorem      Me.84
Integrals or Integration by differentiating under the sign of integration      2258
Integrals or Integration by elliptic functions      G.11 L.46
Integrals or Integration by Pfaff's method      A.47
Integrals or Integration by series      Me.71
Integrals or Integration by substitution      A.18
Integrals or Integration by Tchebychef's method      L.74 M.5
Integrals or Integration by the principle of Abel's derivative      J.23
Integrals or Integration for quadrature of curves      5205—5211 C.68 70
Integrals or Integration for quadrature of curves, circle      J.21 23 JP.27
Integrals or Integration for quadrature of curves, triple integrals      J.59
Integrals or Integration from orthogonal surfaces' theory      L.38
Integrals or Integration of a closed curve      5204 C.23 E.28 Z.17
Integrals or Integration of a complex function      A.66
Integrals or Integration of a complex function, th of Cauchy      Ac.84
Integrals or Integration of alg. differentials by means of logarithms      Mo.57 An.75 C.90 J.12 24 78 79 Mo.84 N.81 see
Integrals or Integration of algebraic surfaces      C.99 J.26
Integrals or Integration of algebraic surfaces, cubature      C.80
Integrals or Integration of algebraic surfaces, octic      An.52
Integrals or Integration of circular functions      1938—1997 2453—2522 No.1799 LM.4 M.6 Mem.9
Integrals or Integration of circular, logarithmic and exponential functions      2571—2643 see
Integrals or Integration of differentials containing the square root of a cubic or biquadratic      Me.57
Integrals or Integration of discontinuous functions      2252 C.23 LM.6
Integrals or Integration of dynamics      L.52 55 58
Integrals or Integration of explicit functions, determination of algebraic part of result      An.61
Integrals or Integration of exponential and logarithmic functions      2391—2431 E.17 18
Integrals or Integration of functions which become infinite between the limits      2240 J.20 JP.11 Q.6
Integrals or Integration of infinite relations      M.14
Integrals or Integration of irrational alg. curves by logarithms      An.61
Integrals or Integration of irrational functions      2110—2120 AJ.2 An.56 C.32 89 L.53 64 Mem.30
Integrals or Integration of rational fractions      1915 CD.3 Mem.33 N.72
Integrals or Integration of rational functions      2021—2032 2071—2103 L.27 N.73
Integrals or Integration of total differentials      C.99
Integrals or Integration of transcendental functions      JP.26
Integrals or Integration of two-membered complete differentials      J.54
Integrals or Integration with imaginary limits      C.23 J.37
Integrals or Integration, approximation to      2127 2262 2991 A.9 14 C.97 CM.2 G.3 J.1 16 18 37 48 L.80
Integrals or Integration, approximation to, Gauss's      2997 C.84 M.25
Integrals or Integration, circular-logarithmic functions, $\frac{x^{p}(log x)^{m}}{x^{2n}-2x^{n}cos n\theta +1}$       2033
Integrals or Integration, circular-logarithmic functions, limits 0 to $\frac{\pi}{2}$ , $log{sin \atop cos}x$ and $log\surd(1-k^{2}sin^{2}x)$ , each with the above denominator      J.92
Integrals or Integration, circular-logarithmic functions, limits 0 to $\frac{\pi}{2}$ , $\frac{log(1+c cos x)}{cos x}$       2633
Integrals or Integration, circular-logarithmic functions, limits 0 to $\frac{\pi}{2}$ , $\frac{log(1+n^{2}sin^{2}x)}{\surd(1-k^{2}sin^{2}x)}$       L.46
Integrals or Integration, circular-logarithmic functions, limits 0 to $\frac{\pi}{2}$ , log sin x      2635 CM.2 E.23 Q.12
Integrals or Integration, circular-logarithmic functions, limits 0 to $\frac{\pi}{2}$ , log sin x, 0 to $n\pi$ and similar integrals      A.16
Integrals or Integration, circular-logarithmic functions, limits 0 to $\frac{\pi}{2}$ , tan x log cosec x      E.27
Integrals or Integration, circular-logarithmic functions, limits 0 to $\frac{\pi}{4}$ , log sin x log cos x, &c.      E.22
Integrals or Integration, circular-logarithmic functions, limits 0 to $\infty$ , $\frac{cos ax}{b^{2}+x^{2}}log 2cx$       A.11
Integrals or Integration, circular-logarithmic functions, limits 0 to $\infty$ , $\frac{log(1-2a cos cx+a^{2})}{1+x^{2}}$       2631
Integrals or Integration, circular-logarithmic functions, limits 0 to $\pi$ , $cos rx log(1-2a cos x+a^{2})$       2625 A.13
Integrals or Integration, circular-logarithmic functions, limits 0 to $\pi$ , $log(1-2a cos x+a^{2})$       2620—2602 L.38 Q.11
Integrals or Integration, circular-logarithmic functions, limits 0 to $\pi$ , $x log sin^{2}x$       2638
Integrals or Integration, circular-logarithmic functions, limits 0 to $\pi$ , $\frac{log(1+c cos x)}{cos x}$       2634
Integrals or Integration, circular-logarithmic functions, limits 0 to $\pi$ , x log sin x      2637
Integrals or Integration, circular-logarithmic functions, limits 0 to 1, $\frac{(1-2x cos\phi +x^{2})}{x(1-x^{2})}, &c.$ 13 similar      L.73
Integrals or Integration, circular-logarithmic functions, limits 0 to 1, $\frac{log(1-2x cos\phi +x^{2})}{x}, &c., &c.$       A.34
Integrals or Integration, circular-logarithmic functions, limits 0 to 1, ${sin \atop cos}(m log x)/log x$ , and similar      2641—2643
Integrals or Integration, circular-logarithmic functions, limits 0 to 1, log sin x log cos x, &c.      E.22
Integrals or Integration, circular-logarithmic functions, other limits, $\int^{2\pi}_{0}F(cos nx)log sin\frac{x}{2}dx$       Z.10
Integrals or Integration, circular-logarithmic functions, other limits, $\int^{a}_{0}\frac{a+b cos x}{a-b cos x}dx$       A.53
Integrals or Integration, circular-logarithmic functions, other limits, $\int^{n\pi}_{0}x^{m}log(1-2a cos x+x^{2})dx$ , and similar      J.40
Integrals or Integration, circular-logarithmic functions, other limits, $\int^{\frac{\pi}{2}}_{0}cos^{2(n-1)}x log tan x dx$       A.16
Integrals or Integration, comparison of transcendents      Me.79 Pr.8
Integrals or Integration, complex, representing products and powers of a definite integral      J.48
Integrals or Integration, connected with trinomial integrals      L.55
Integrals or Integration, convergency of      M.13
Integrals or Integration, definite, applied to Euler's, &c.      J.16
Integrals or Integration, definite, from indefinite      J.41 51 52
Integrals or Integration, definite, with finite differences      J.12
Integrals or Integration, determination of functions under the sign $\int$       JP.15
Integrals or Integration, difference between a sum and an integral      2230 G.9
Integrals or Integration, division into others of smaller intervals      A.4
Integrals or Integration, eight rules for definite integration      2245
Integrals or Integration, equations for obtaining functions as integrals      J.79
Integrals or Integration, exponential-logarithmic functions, $\int^{2n_{\pi}}_{0}e^{cx-}log(1-2a cos x+a^{2})dx$       J.40
Integrals or Integration, exponential-logarithmic functions, $\int^{\infty}_{0}\frac{e^{ax}-e^{-ax}}{e^{\pi x}-e^{-\pi x}}log(x^{2}+u^{2})dx, &c.$       J.38
Integrals or Integration, expressible only by logarithms      An.76
Integrals or Integration, extended independently of the conception of differentials      A.61
Integrals or Integration, formulae of      A.1 J.18 19 M.4 Me.76 Mo.85 N.85
Integrals or Integration, formulae of, failure of f      CM.2
Integrals or Integration, higher, of composite functions      A.20
Integrals or Integration, indefinite algebraic functions, $F(\surd X_{3})$       L.57
Integrals or Integration, indefinite algebraic functions, $x^{2n}F\left\{(ax-\frac{b}{x})^{2}\right\}$ (Cauchy)      2712 A.9
Integrals or Integration, indefinite algebraic functions, $x^{m}(a+bx^{n})^{p}$       2035—2060 A.36 Mem.11
Integrals or Integration, indefinite algebraic functions, $\frac{(1\pm x^{2})^{2}}{(1\pm x^{2})(1+bx^{2}+x^{4})^{2}}$       Mem.10
Integrals or Integration, indefinite algebraic functions, $\frac{1}{(1-x^{3})^{\frac{2}{3}}}$       Me.82
Integrals or Integration, indefinite algebraic functions, $\frac{1}{(x-a)^{p}(x-b)^{q}}$       A.40
Integrals or Integration, indefinite algebraic functions, $\frac{1}{(x^{3}-1)\surd(x^{3}-b^{3})}\, &c.$ , reduced to Jacobi's functions      Q.18
Integrals or Integration, indefinite algebraic functions, $\frac{1}{x^{2}+a^{2}}$       2061—2065 J.36
Integrals or Integration, indefinite algebraic functions, $\frac{1}{x^{n}(x-1)^{n}}$       2007
Integrals or Integration, indefinite algebraic functions, $\frac{1}{\surd X_{3}}$       2141 J.17 Man.79
Integrals or Integration, indefinite algebraic functions, $\frac{1}{\surd X_{4}}$       C.59 CD.1 E.36 J.10
Integrals or Integration, indefinite algebraic functions, $\frac{f(x)}{F(x)\surd X_{4}}$       C.51
Integrals or Integration, indefinite algebraic functions, $\frac{f(x)}{\surd\pm(1-x^{8})}$       J.32
Integrals or Integration, indefinite algebraic functions, $\frac{x+a}{\surd X_{4}}$       L.64 Mel.3
Integrals or Integration, indefinite algebraic functions, $\frac{x^{a-1}(1+x^{2})}{1+x^{4n+2}}$ , and 12 similar      A.35
Integrals or Integration, indefinite algebraic functions, $\frac{x^{a-1}}{1+x^{2}+...+x^{2(n-1)}}, &c.$       A.16
Integrals or Integration, indefinite algebraic functions, $\frac{x^{m}}{x^{n}\pm 1}$ and deductions      2021—2028
Integrals or Integration, indefinite algebraic functions, $\frac{x^{n}}{1+2xcos\phi+x^{2}}$       A.12 E.41
Integrals or Integration, indefinite algebraic functions, $\frac{x^{n}}{1+2xcos\phi+x^{2}}$ , deductions from this involving integrals of the forms $\int^{1}_{0}\frac{1-x^{n}}{1-x}dx\, and\, \int^{\beta}_{a}\frac{sin\frac{ma\pi}{n}}{sin a\pi}$       A.35
Integrals or Integration, indefinite algebraic functions, $\frac{x}{(x^{3}+8)\surd(x^{3}-1)}$       A.3
Integrals or Integration, indefinite algebraic functions, fractions involving a binomial surd      2008—2019
Integrals or Integration, indefinite algebraic functions, fractions involving a binomial surd, $\frac{1}{(1+x)\sqrt[4]{}{(2x^{2}-1)}}$       Mem.13
Integrals or Integration, indefinite algebraic functions, fractions involving a binomial surd, $\frac{x^{m}}{(x^{n}-a)\surd(x^{n}-b)}$       Q.18
Integrals or Integration, indefinite algebraic functions, fractions involving a binomial surd, $\frac{\surd(1+x^{4})}{1-x^{4}}$       2015 L.80 Z.8
Integrals or Integration, indefinite algebraic functions, functions of $(a+bx+cx^{2})$       2071—2080 2103—2109
Integrals or Integration, indefinite algebraic functions, functions of $(a+bx+cx^{2})$ , $\frac{x^{m}}{\sqrt[3]{}{(a+bx+cx^{2})^{n}}}$       A.55
Integrals or Integration, indefinite algebraic functions, functions of $(a+bx^{2}+cx^{4})$       2081—2085
Integrals or Integration, indefinite algebraic functions, functions of $(a+bx^{n}+cx^{2n})$       2086—2102
Integrals or Integration, indefinite algebraic functions, limits 0 to $\infty$ , $X{}^{n}x^{-r}$       Me.83
Integrals or Integration, indefinite algebraic functions, limits 0 to $\infty$ , $\frac{1}{(x^{2}+a^{2})^{n}}$       2364
Integrals or Integration, indefinite algebraic functions, limits 0 to $\infty$ , $\frac{x^{a-1}}{1+x^{n}+x^{2n}}, 2n>a>0$       N.48
Integrals or Integration, indefinite algebraic functions, limits 0 to $\infty$ , $\frac{x^{m}}{1\pm x}\, , &c.$       2309—2312 2345—2355 A.38 J.24 L.41 Q.12 Z.19
Integrals or Integration, indefinite algebraic functions, limits 0 to 1, $x^{l-1}(1-x)^{m-1}$       2280 A.40 C.16 J.11 17
Integrals or Integration, indefinite algebraic functions, limits 0 to 1, $\frac{1}{(a-bx)^{m}(1-x)^{1-n}x^{n}}$       J.42
Integrals or Integration, indefinite algebraic functions, limits 0 to 1, $\frac{x^{a-1}}{1-x}-\frac{nx^{na-1}}{1-x^{n}}$       2367 A.10
Integrals or Integration, indefinite algebraic functions, limits 0 to 1, $\frac{x^{l-1}+x^{m-1}}{(1+x)^{l+m}}$       2341 C.55
Integrals or Integration, indefinite algebraic functions, limits 0 to 1, $\frac{x^{m+\frac{1}{2}(1-x)^{m-\frac{1}{2}}}}{(a+bx+cx^{2})^{m+1}}$       L.56—57
Integrals or Integration, indefinite algebraic functions, limits 0 to 1, $\frac{x^{m}(1-x)^{n}}{(1+ax)^{p}}$       L.59
Integrals or Integration, indefinite algebraic functions, limits 0 to 1, $\frac{x^{p}(1-x)^{q}}{\{1+\surd(1+ax)\}^{2p+2q+2}}$       L.57
Integrals or Integration, indefinite algebraic functions, limits 0 to 1, Euler's      see "Euler's integrals"
Integrals or Integration, indefinite algebraic functions, limits 0 to 1, similar forms      2342—2444 2352 2356—2367
Integrals or Integration, indefinite algebraic functions, other limits, $\int^{1}_{-1}\frac{F(x)dx}{\surd(1-x^{2})}$ , $\int^{b}\frac{F(x)dx}{(x-c)^{n}}$       2368—2369
Integrals or Integration, indefinite algebraic functions, other limits, $\int^{1}_{-1}\frac{sin a}{1-2xcos a+x^{2}}dx=f(a)$       geoN.85
Integrals or Integration, indefinite algebraic functions, other limits, $\int^{\sqrt[n]{}\frac{a}{b}}_{0}(a-bx)^{\frac{p}{q}}x^{m-1}dx$       A.35
Integrals or Integration, indefinite algebraic functions, rational algebraic functions of irrational ones, integrated by rationalizing      2110—2120
Integrals or Integration, indefinite algebraic functions, reducible to elliptic integrals, viz., $F(x, \surd X_{4})$       2121 LM.8 L.57
Integrals or Integration, indefinite algebraic functions, reducible to elliptic integrals, viz., $\frac{F(x)}{\surd X_{4}}$       2133—2136 J.36 LM.14
Integrals or Integration, indefinite algebraic functions, reducible to elliptic integrals, viz., rational functions of $\surd X_{4}$ , $\surd X_{3}$ , and $\surd X_{6}$ , where $X_{4}$ is a quartic in x      2121—2141
Integrals or Integration, indefinite algebraic functions, simple functions of $x^{2}\pm a^{2}$       1926—1937
Integrals or Integration, indefinite algebraic functions, simple functions of $x^{m}$       A.4
Integrals or Integration, indefinite algebraic functions, simple functions of $\frac{1}{x^{2}+a^{2}}$       N.82
Integrals or Integration, indefinite algebraic functions, simple functions of $\frac{x^{m}}{\surd(1-x^{2})}$       An.68
Integrals or Integration, indefinite algebraic functions, simple functions of $\surd(a^{2}-x^{2})$       A.38
Integrals or Integration, indefinite algebraic functions, sundry      CM.2 L.47
Integrals or Integration, indefinite algebraic functions, unclassified      An.75 C.90 J.12 24 78 79 Mo.84 N.81
Integrals or Integration, indefinite circular functions, $(a+2bcos x+c cos 2x)^{-1}$       1993
Integrals or Integration, indefinite circular functions, $(a+2bcos x+c cos 2x)^{-1}$ , $\frac{x^{m}}{x^{2n}-2x^{n}cos n\theta+1}$       2029
Integrals or Integration, indefinite circular functions, $(sin amx)^{2n}$       J.81
Integrals or Integration, indefinite circular functions, $cos^{n}x$       N.74

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