3.2 Integrals 101 to 195

\(\int (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}) \, dx\) [101]
\(\int (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2 \, dx\) [102]
\(\int (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^3 \, dx\) [103]
\(\int \genfrac {}{}{}{}{x^3}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [104]
\(\int \genfrac {}{}{}{}{x^2}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [105]
\(\int \genfrac {}{}{}{}{x}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [106]
\(\int \genfrac {}{}{}{}{1}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [107]
\(\int \genfrac {}{}{}{}{1}{x (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})} \, dx\) [108]
\(\int \genfrac {}{}{}{}{1}{x^2 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})} \, dx\) [109]
\(\int \genfrac {}{}{}{}{1}{x^3 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})} \, dx\) [110]
\(\int \genfrac {}{}{}{}{x^3}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [111]
\(\int \genfrac {}{}{}{}{x^2}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [112]
\(\int \genfrac {}{}{}{}{x}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [113]
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [114]
\(\int \genfrac {}{}{}{}{1}{x (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [115]
\(\int \genfrac {}{}{}{}{1}{x^2 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [116]
\(\int \genfrac {}{}{}{}{1}{x^3 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [117]
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^3} \, dx\) [118]
\(\int \genfrac {}{}{}{}{x}{(1+(x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [119]
\(\int x^3 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [120]
\(\int x^2 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [121]
\(\int x (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [122]
\(\int (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [123]
\(\int \genfrac {}{}{}{}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p}{x} \, dx\) [124]
\(\int \genfrac {}{}{}{}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p}{x^2} \, dx\) [125]
\(\int (a+b (c x^n)^{2/n})^3 \, dx\) [126]
\(\int (a+b (c x^n)^{2/n})^2 \, dx\) [127]
\(\int (a+b (c x^n)^{2/n}) \, dx\) [128]
\(\int \genfrac {}{}{}{}{1}{a+b (c x^n)^{2/n}} \, dx\) [129]
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{2/n})^2} \, dx\) [130]
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{2/n})^3} \, dx\) [131]
\(\int \genfrac {}{}{}{}{1}{1+4 \sqrt {x^4}} \, dx\) [132]
\(\int \genfrac {}{}{}{}{1}{1-4 \sqrt {x^4}} \, dx\) [133]
\(\int \genfrac {}{}{}{}{1}{1+4 \sqrt [3]{x^6}} \, dx\) [134]
\(\int \genfrac {}{}{}{}{1}{1-4 \sqrt [3]{x^6}} \, dx\) [135]
\(\int \genfrac {}{}{}{}{1}{1+4 (x^{2 n})^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [136]
\(\int \genfrac {}{}{}{}{1}{1-4 (x^{2 n})^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [137]
\(\int (a+b (c x^n)^{3/n})^3 \, dx\) [138]
\(\int (a+b (c x^n)^{3/n})^2 \, dx\) [139]
\(\int (a+b (c x^n)^{3/n}) \, dx\) [140]
\(\int \genfrac {}{}{}{}{1}{a+b (c x^n)^{3/n}} \, dx\) [141]
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{3/n})^2} \, dx\) [142]
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{3/n})^3} \, dx\) [143]
\(\int (d x)^m (a+b (c x^q)^n)^p \, dx\) [144]
\(\int x^2 (a+b (c x^q)^n)^p \, dx\) [145]
\(\int x (a+b (c x^q)^n)^p \, dx\) [146]
\(\int (a+b (c x^q)^n)^p \, dx\) [147]
\(\int \genfrac {}{}{}{}{(a+b (c x^q)^n)^p}{x} \, dx\) [148]
\(\int \genfrac {}{}{}{}{(a+b (c x^q)^n)^p}{x^2} \, dx\) [149]
\(\int \sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^2 \, dx\) [150]
\(\int \sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x \, dx\) [151]
\(\int \sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} \, dx\) [152]
\(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}}{x} \, dx\) [153]
\(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}}{x^2} \, dx\) [154]
\(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}}{x^3} \, dx\) [155]
\(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}}{x^4} \, dx\) [156]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}} \, dx\) [157]
\(\int \genfrac {}{}{}{}{x}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}} \, dx\) [158]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}} \, dx\) [159]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x} \, dx\) [160]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^2} \, dx\) [161]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^3} \, dx\) [162]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^4} \, dx\) [163]
\(\int \sqrt {\sqrt {\genfrac {}{}{}{}{1}{x}}+\genfrac {}{}{}{}{1}{x}} \, dx\) [164]
\(\int \sqrt {2+\sqrt {\genfrac {}{}{}{}{1}{x}}+\genfrac {}{}{}{}{1}{x}} \, dx\) [165]
\(\int \sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^m \, dx\) [166]
\(\int \genfrac {}{}{}{}{x^m}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}} \, dx\) [167]
\(\int (c x^n)^{\genfrac {}{}{}{}{1}{n}} (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [168]
\(\int (c x^n)^{\genfrac {}{}{}{}{1}{n}} (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^3 \, dx\) [169]
\(\int (c x^n)^{\genfrac {}{}{}{}{1}{n}} (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2 \, dx\) [170]
\(\int (c x^n)^{\genfrac {}{}{}{}{1}{n}} (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}) \, dx\) [171]
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [172]
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [173]
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^3} \, dx\) [174]
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^4} \, dx\) [175]
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^5} \, dx\) [176]
\(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b x}} \, dx\) [177]
\(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b (c x)^m}} \, dx\) [178]
\(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b (c (d x)^m)^n}} \, dx\) [179]
\(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b (c (d (e x)^m)^n)^p}} \, dx\) [180]
\(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}} (-1+x^2)^3}{x} \, dx\) [181]
\(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}} (-1+x^2)^2}{x} \, dx\) [182]
\(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}} (-1+x^2)}{x} \, dx\) [183]
\(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}}}{x (-1+x^2)} \, dx\) [184]
\(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}}}{x (-1+x^2)^2} \, dx\) [185]
\(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}}}{x (-1+x^2)^3} \, dx\) [186]
\(\int \genfrac {}{}{}{}{\sqrt {1+\genfrac {}{}{}{}{1}{x^2}} x}{(1+x^2)^2} \, dx\) [187]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+\genfrac {}{}{}{}{1}{x^2}} x (1+x^2)} \, dx\) [188]
\(\int \genfrac {}{}{}{}{x}{a+b x^2+\sqrt {a+b x^2}} \, dx\) [189]
\(\int \genfrac {}{}{}{}{x}{x^2-\sqrt [3]{x^2}} \, dx\) [190]
\(\int x^5 \sqrt {1-x^3} (1+x^9)^2 \, dx\) [191]
\(\int (\genfrac {}{}{}{}{x}{(a+b x^2)^{3/2}}+\genfrac {}{}{}{}{x}{(1+x^2) \sqrt {a+b x^2}}) \, dx\) [192]
\(\int \genfrac {}{}{}{}{x (1+a+x^2+b x^2)}{(1+x^2) (a+b x^2)^{3/2}} \, dx\) [193]
\(\int (\genfrac {}{}{}{}{x}{(a+b x^2)^{5/2}}+\genfrac {}{}{}{}{x}{(a+b x^2)^{3/2}}+\genfrac {}{}{}{}{x}{(1+x^2) \sqrt {a+b x^2}}) \, dx\) [194]
\(\int \genfrac {}{}{}{}{x (1+a+a^2+x^2+a x^2+b x^2+2 a b x^2+b x^4+b^2 x^4)}{(1+x^2) (a+b x^2)^{5/2}} \, dx\) [195]