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3.2
Integrals 101 to 200
\(\int x \cot ^{-1}(a+b x) \, dx\) [101]
\(\int \cot ^{-1}(a+b x) \, dx\) [102]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{x} \, dx\) [103]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{x^2} \, dx\) [104]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{x^3} \, dx\) [105]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{x^4} \, dx\) [106]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{c+d x^2} \, dx\) [107]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{c+d x} \, dx\) [108]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{c+\genfrac {}{}{}{}{d}{x}} \, dx\) [109]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{c+\genfrac {}{}{}{}{d}{x^2}} \, dx\) [110]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{c+d \sqrt {x}} \, dx\) [111]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{c+\genfrac {}{}{}{}{d}{\sqrt {x}}} \, dx\) [112]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(d+e x)}{a+b x+c x^2} \, dx\) [113]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{\sqrt {1+a^2+2 a b x+b^2 x^2}} \, dx\) [114]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{\sqrt {(1+a^2) c+2 a b c x+b^2 c x^2}} \, dx\) [115]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{\sqrt [3]{1+a^2+2 a b x+b^2 x^2}} \, dx\) [116]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{\sqrt [3]{(1+a^2) c+2 a b c x+b^2 c x^2}} \, dx\) [117]
\(\int \genfrac {}{}{}{}{(a+b x)^2 \cot ^{-1}(a+b x)}{\sqrt {1+a^2+2 a b x+b^2 x^2}} \, dx\) [118]
\(\int \genfrac {}{}{}{}{(a+b x)^2 \cot ^{-1}(a+b x)}{\sqrt {(1+a^2) c+2 a b c x+b^2 c x^2}} \, dx\) [119]
\(\int \genfrac {}{}{}{}{(a+b x)^2 \cot ^{-1}(a+b x)}{\sqrt [3]{1+a^2+2 a b x+b^2 x^2}} \, dx\) [120]
\(\int \genfrac {}{}{}{}{(a+b x)^2 \cot ^{-1}(a+b x)}{\sqrt [3]{(1+a^2) c+2 a b c x+b^2 c x^2}} \, dx\) [121]
\(\int (a+b x)^2 \cot ^{-1}(a+b x) \, dx\) [122]
\(\int (a+b x) \cot ^{-1}(a+b x) \, dx\) [123]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{a+b x} \, dx\) [124]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{(a+b x)^2} \, dx\) [125]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(1+x)}{2+2 x} \, dx\) [126]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(a+b x)}{\genfrac {}{}{}{}{a d}{b}+d x} \, dx\) [127]
\(\int (a+b x)^2 \sqrt {\cot ^{-1}(a+b x)} \, dx\) [128]
\(\int (e+f x)^3 (a+b \cot ^{-1}(c+d x)) \, dx\) [129]
\(\int (e+f x)^2 (a+b \cot ^{-1}(c+d x)) \, dx\) [130]
\(\int (e+f x) (a+b \cot ^{-1}(c+d x)) \, dx\) [131]
\(\int (a+b \cot ^{-1}(c+d x)) \, dx\) [132]
\(\int \genfrac {}{}{}{}{a+b \cot ^{-1}(c+d x)}{e+f x} \, dx\) [133]
\(\int \genfrac {}{}{}{}{a+b \cot ^{-1}(c+d x)}{(e+f x)^2} \, dx\) [134]
\(\int \genfrac {}{}{}{}{a+b \cot ^{-1}(c+d x)}{(e+f x)^3} \, dx\) [135]
\(\int (e+f x)^2 (a+b \cot ^{-1}(c+d x))^2 \, dx\) [136]
\(\int (e+f x) (a+b \cot ^{-1}(c+d x))^2 \, dx\) [137]
\(\int (a+b \cot ^{-1}(c+d x))^2 \, dx\) [138]
\(\int \genfrac {}{}{}{}{(a+b \cot ^{-1}(c+d x))^2}{e+f x} \, dx\) [139]
\(\int \genfrac {}{}{}{}{(a+b \cot ^{-1}(c+d x))^2}{(e+f x)^2} \, dx\) [140]
\(\int (e+f x)^2 (a+b \cot ^{-1}(c+d x))^3 \, dx\) [141]
\(\int (e+f x) (a+b \cot ^{-1}(c+d x))^3 \, dx\) [142]
\(\int (a+b \cot ^{-1}(c+d x))^3 \, dx\) [143]
\(\int \genfrac {}{}{}{}{(a+b \cot ^{-1}(c+d x))^3}{e+f x} \, dx\) [144]
\(\int \genfrac {}{}{}{}{(a+b \cot ^{-1}(c+d x))^3}{(e+f x)^2} \, dx\) [145]
\(\int (e+f x)^m (a+b \cot ^{-1}(c+d x)) \, dx\) [146]
\(\int (e+f x)^m (a+b \cot ^{-1}(c+d x))^2 \, dx\) [147]
\(\int (e+f x)^m (a+b \cot ^{-1}(c+d x))^3 \, dx\) [148]
\(\int x^3 \cot ^{-1}(a+b x^4) \, dx\) [149]
\(\int x^{-1+n} \cot ^{-1}(a+b x^n) \, dx\) [150]
\(\int \genfrac {}{}{}{}{(a+b \cot ^{-1}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))^n}{1-c^2 x^2} \, dx\) [151]
\(\int \genfrac {}{}{}{}{(a+b \cot ^{-1}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))^3}{1-c^2 x^2} \, dx\) [152]
\(\int \genfrac {}{}{}{}{(a+b \cot ^{-1}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))^2}{1-c^2 x^2} \, dx\) [153]
\(\int \genfrac {}{}{}{}{a+b \cot ^{-1}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}})}{1-c^2 x^2} \, dx\) [154]
\(\int \genfrac {}{}{}{}{1}{(1-c^2 x^2) (a+b \cot ^{-1}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))} \, dx\) [155]
\(\int \genfrac {}{}{}{}{1}{(1-c^2 x^2) (a+b \cot ^{-1}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))^2} \, dx\) [156]
\(\int \cot ^{-1}(\tan (a+b x)) \, dx\) [157]
\(\int x^2 \cot ^{-1}(c+d \tan (a+b x)) \, dx\) [158]
\(\int x \cot ^{-1}(c+d \tan (a+b x)) \, dx\) [159]
\(\int \cot ^{-1}(c+d \tan (a+b x)) \, dx\) [160]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(c+d \tan (a+b x))}{x} \, dx\) [161]
\(\int x^2 \cot ^{-1}(c+(1+i c) \tan (a+b x)) \, dx\) [162]
\(\int x \cot ^{-1}(c+(1+i c) \tan (a+b x)) \, dx\) [163]
\(\int \cot ^{-1}(c+(1+i c) \tan (a+b x)) \, dx\) [164]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(c+(1+i c) \tan (a+b x))}{x} \, dx\) [165]
\(\int x^2 \cot ^{-1}(c-(1-i c) \tan (a+b x)) \, dx\) [166]
\(\int x \cot ^{-1}(c-(1-i c) \tan (a+b x)) \, dx\) [167]
\(\int \cot ^{-1}(c-(1-i c) \tan (a+b x)) \, dx\) [168]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx\) [169]
\(\int \cot ^{-1}(\cot (a+b x)) \, dx\) [170]
\(\int x^2 \cot ^{-1}(c+d \cot (a+b x)) \, dx\) [171]
\(\int x \cot ^{-1}(c+d \cot (a+b x)) \, dx\) [172]
\(\int \cot ^{-1}(c+d \cot (a+b x)) \, dx\) [173]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(c+d \cot (a+b x))}{x} \, dx\) [174]
\(\int x^2 \cot ^{-1}(c+(1-i c) \cot (a+b x)) \, dx\) [175]
\(\int x \cot ^{-1}(c+(1-i c) \cot (a+b x)) \, dx\) [176]
\(\int \cot ^{-1}(c+(1-i c) \cot (a+b x)) \, dx\) [177]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(c+(1-i c) \cot (a+b x))}{x} \, dx\) [178]
\(\int x^2 \cot ^{-1}(c-(1+i c) \cot (a+b x)) \, dx\) [179]
\(\int x \cot ^{-1}(c-(1+i c) \cot (a+b x)) \, dx\) [180]
\(\int \cot ^{-1}(c-(1+i c) \cot (a+b x)) \, dx\) [181]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(c-(1+i c) \cot (a+b x))}{x} \, dx\) [182]
\(\int (e+f x)^3 \cot ^{-1}(\tanh (a+b x)) \, dx\) [183]
\(\int (e+f x)^2 \cot ^{-1}(\tanh (a+b x)) \, dx\) [184]
\(\int (e+f x) \cot ^{-1}(\tanh (a+b x)) \, dx\) [185]
\(\int \cot ^{-1}(\tanh (a+b x)) \, dx\) [186]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(\tanh (a+b x))}{e+f x} \, dx\) [187]
\(\int x^2 \cot ^{-1}(c+d \tanh (a+b x)) \, dx\) [188]
\(\int x \cot ^{-1}(c+d \tanh (a+b x)) \, dx\) [189]
\(\int \cot ^{-1}(c+d \tanh (a+b x)) \, dx\) [190]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(c+d \tanh (a+b x))}{x} \, dx\) [191]
\(\int x^2 \cot ^{-1}(c+(i+c) \tanh (a+b x)) \, dx\) [192]
\(\int x \cot ^{-1}(c+(i+c) \tanh (a+b x)) \, dx\) [193]
\(\int \cot ^{-1}(c+(i+c) \tanh (a+b x)) \, dx\) [194]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(c+(i+c) \tanh (a+b x))}{x} \, dx\) [195]
\(\int x^2 \cot ^{-1}(c-(i-c) \tanh (a+b x)) \, dx\) [196]
\(\int x \cot ^{-1}(c-(i-c) \tanh (a+b x)) \, dx\) [197]
\(\int \cot ^{-1}(c-(i-c) \tanh (a+b x)) \, dx\) [198]
\(\int \genfrac {}{}{}{}{\cot ^{-1}(c-(i-c) \tanh (a+b x))}{x} \, dx\) [199]
\(\int (e+f x)^3 \cot ^{-1}(\coth (a+b x)) \, dx\) [200]
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