3.2 Integrals 101 to 178

\(\int \genfrac {}{}{}{}{b e+2 c e x+3 d e x^2}{(a+b x+c x^2+d x^3)^2} \, dx\) [101]
\(\int \genfrac {}{}{}{}{b e+2 c e x+3 d e x^2}{(a+b x+c x^2+d x^3)^3} \, dx\) [102]
\(\int (b e+2 c e x+3 d e x^2) (a+b x+c x^2+d x^3)^{3/2} \, dx\) [103]
\(\int (b e+2 c e x+3 d e x^2) \sqrt {a+b x+c x^2+d x^3} \, dx\) [104]
\(\int \genfrac {}{}{}{}{b e+2 c e x+3 d e x^2}{\sqrt {a+b x+c x^2+d x^3}} \, dx\) [105]
\(\int \genfrac {}{}{}{}{b e+2 c e x+3 d e x^2}{(a+b x+c x^2+d x^3)^{3/2}} \, dx\) [106]
\(\int \genfrac {}{}{}{}{b e+2 c e x+3 d e x^2}{(a+b x+c x^2+d x^3)^{5/2}} \, dx\) [107]
\(\int (b e+2 c e x+3 d e x^2) (a+b x+c x^2+d x^3)^p \, dx\) [108]
\(\int (A+B x+C x^2) (a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3)^3 \, dx\) [109]
\(\int (A+B x+C x^2) (a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3)^2 \, dx\) [110]
\(\int (A+B x+C x^2) (a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3) \, dx\) [111]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3} \, dx\) [112]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3)^2} \, dx\) [113]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3)^3} \, dx\) [114]
\(\int (A+B x+C x^2) \sqrt {a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3} \, dx\) [115]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{\sqrt {a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3}} \, dx\) [116]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3)^{3/2}} \, dx\) [117]
\(\int (A+B x+C x^2) (70+67 x-53 x^2+6 x^3)^{3/2} \, dx\) [118]
\(\int (A+B x+C x^2) \sqrt {70+67 x-53 x^2+6 x^3} \, dx\) [119]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{\sqrt {70+67 x-53 x^2+6 x^3}} \, dx\) [120]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{(70+67 x-53 x^2+6 x^3)^{3/2}} \, dx\) [121]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{(70+67 x-53 x^2+6 x^3)^{5/2}} \, dx\) [122]
\(\int ((a+b x) (c+d x) (e+f x))^p (A+B x+C x^2) \, dx\) [123]
\(\int (A+B x+C x^2) (a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3)^p \, dx\) [124]
\(\int (A+B x+C x^2) (a d+(b d+a e) x+(c d+b e) x^2+c e x^3)^2 \, dx\) [125]
\(\int (A+B x+C x^2) (a d+(b d+a e) x+(c d+b e) x^2+c e x^3) \, dx\) [126]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{a d+(b d+a e) x+(c d+b e) x^2+c e x^3} \, dx\) [127]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{(a d+(b d+a e) x+(c d+b e) x^2+c e x^3)^2} \, dx\) [128]
\(\int (A+B x+C x^2) \sqrt {a d+(b d+a e) x+(c d+b e) x^2+c e x^3} \, dx\) [129]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{\sqrt {a d+(b d+a e) x+(c d+b e) x^2+c e x^3}} \, dx\) [130]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{(a d+(b d+a e) x+(c d+b e) x^2+c e x^3)^{3/2}} \, dx\) [131]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{\sqrt {8-8 x+4 x^2-x^3}} \, dx\) [132]
\(\int (A+B x+C x^2) (a d+(b d+a e) x+(c d+b e) x^2+c e x^3)^p \, dx\) [133]
\(\int (e+f x)^2 (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3) \, dx\) [134]
\(\int (e+f x) (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3) \, dx\) [135]
\(\int (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3) \, dx\) [136]
\(\int \genfrac {}{}{}{}{1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}{e+f x} \, dx\) [137]
\(\int \genfrac {}{}{}{}{1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}{(e+f x)^2} \, dx\) [138]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3} \, dx\) [139]
\(\int \genfrac {}{}{}{}{(e+f x)^2}{1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3} \, dx\) [140]
\(\int \genfrac {}{}{}{}{e+f x}{1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3} \, dx\) [141]
\(\int \genfrac {}{}{}{}{1}{1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3} \, dx\) [142]
\(\int \genfrac {}{}{}{}{1}{(e+f x) (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)} \, dx\) [143]
\(\int \genfrac {}{}{}{}{1}{(e+f x)^2 (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)} \, dx\) [144]
\(\int \genfrac {}{}{}{}{(e+f x)^2}{(1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^2} \, dx\) [145]
\(\int \genfrac {}{}{}{}{e+f x}{(1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^2} \, dx\) [146]
\(\int \genfrac {}{}{}{}{1}{(1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^2} \, dx\) [147]
\(\int \genfrac {}{}{}{}{1}{(e+f x) (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^2} \, dx\) [148]
\(\int \genfrac {}{}{}{}{1}{(e+f x)^2 (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^2} \, dx\) [149]
\(\int (e+f x)^2 \sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3} \, dx\) [150]
\(\int (e+f x) \sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3} \, dx\) [151]
\(\int \sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3} \, dx\) [152]
\(\int \genfrac {}{}{}{}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}}{e+f x} \, dx\) [153]
\(\int \genfrac {}{}{}{}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}}{(e+f x)^2} \, dx\) [154]
\(\int \genfrac {}{}{}{}{(e+f x)^2}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx\) [155]
\(\int \genfrac {}{}{}{}{e+f x}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx\) [156]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx\) [157]
\(\int \genfrac {}{}{}{}{1}{(e+f x) \sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx\) [158]
\(\int \genfrac {}{}{}{}{1}{(e+f x)^2 \sqrt {1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3}} \, dx\) [159]
\(\int \genfrac {}{}{}{}{(e+f x)^2}{(1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^{3/2}} \, dx\) [160]
\(\int \genfrac {}{}{}{}{e+f x}{(1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^{3/2}} \, dx\) [161]
\(\int \genfrac {}{}{}{}{1}{(1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^{3/2}} \, dx\) [162]
\(\int \genfrac {}{}{}{}{1}{(e+f x) (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^{3/2}} \, dx\) [163]
\(\int \genfrac {}{}{}{}{1}{(e+f x)^2 (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3)^{3/2}} \, dx\) [164]
\(\int (A+B x+C x^2) (2+3 x-5 x^2+x^3)^3 \, dx\) [165]
\(\int (A+B x+C x^2) (2+3 x-5 x^2+x^3)^2 \, dx\) [166]
\(\int (A+B x+C x^2) (2+3 x-5 x^2+x^3) \, dx\) [167]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{2+3 x-5 x^2+x^3} \, dx\) [168]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{(2+3 x-5 x^2+x^3)^2} \, dx\) [169]
\(\int (A+B x+C x^2) (2+3 x-5 x^2+x^3)^p \, dx\) [170]
\(\int (A+B x+C x^2) (2+3 x+4 x^2+x^3)^3 \, dx\) [171]
\(\int (A+B x+C x^2) (2+3 x+4 x^2+x^3)^2 \, dx\) [172]
\(\int (A+B x+C x^2) (2+3 x+4 x^2+x^3) \, dx\) [173]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{2+3 x+4 x^2+x^3} \, dx\) [174]
\(\int \genfrac {}{}{}{}{A+B x+C x^2}{(2+3 x+4 x^2+x^3)^2} \, dx\) [175]
\(\int (A+B x+C x^2) (2+3 x+4 x^2+x^3)^p \, dx\) [176]
\(\int \genfrac {}{}{}{}{18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx\) [177]
\(\int \genfrac {}{}{}{}{b e-a f+2 c e x+(3 d e+c f) x^2+2 d f x^3}{(a+b x+c x^2+d x^3)^2} \, dx\) [178]