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3.2
Integrals 101 to 175
3.2.1
\(\int \genfrac {}{}{}{}{e^x}{1+e^{2 x}} \, dx\) [101]
3.2.2
\(\int e^{-x} \cot ^{-1}(e^x) \, dx\) [102]
3.2.3
\(\int \sqrt {\genfrac {}{}{}{}{a+x}{a-x}} \, dx\) [103]
3.2.4
\(\int \sqrt {(b-x) (-a+x)} \, dx\) [104]
3.2.5
\(\int \genfrac {}{}{}{}{1}{\sqrt {(b-x) (-a+x)}} \, dx\) [105]
3.2.6
\(\int \genfrac {}{}{}{}{3+5 x}{-3+2 x+x^2} \, dx\) [106]
3.2.7
\(\int \genfrac {}{}{}{}{5+2 x}{-3+2 x+x^2} \, dx\) [107]
3.2.8
\(\int \genfrac {}{}{}{}{3 x+x^3}{-3-2 x+x^2} \, dx\) [108]
3.2.9
\(\int \genfrac {}{}{}{}{-1+5 x+2 x^2}{-2 x+x^2+x^3} \, dx\) [109]
3.2.10
\(\int \genfrac {}{}{}{}{3+2 x+x^2}{(-1+x) (1+x)^2} \, dx\) [110]
3.2.11
\(\int \genfrac {}{}{}{}{-2+2 x+3 x^2}{-1+x^3} \, dx\) [111]
3.2.12
\(\int \genfrac {}{}{}{}{2-x+2 x^2-x^3+x^4}{(-1+x) (2+x^2)^2} \, dx\) [112]
3.2.13
\(\int \genfrac {}{}{}{}{1}{\cos (x)+\sin (x)} \, dx\) [113]
3.2.14
\(\int \genfrac {}{}{}{}{x}{4-x^2+\sqrt {4-x^2}} \, dx\) [114]
3.2.15
\(\int \genfrac {}{}{}{}{3+2 x}{(-2+x) (5+x)} \, dx\) [115]
3.2.16
\(\int \genfrac {}{}{}{}{x}{(1+x) (2+x) (3+x)} \, dx\) [116]
3.2.17
\(\int \genfrac {}{}{}{}{x}{2-3 x+x^3} \, dx\) [117]
3.2.18
\(\int \genfrac {}{}{}{}{-6+2 x+x^4}{-2 x+x^2+x^3} \, dx\) [118]
3.2.19
\(\int \genfrac {}{}{}{}{7+8 x^3}{(1+x) (1+2 x)^3} \, dx\) [119]
3.2.20
\(\int \genfrac {}{}{}{}{1+x+4 x^2}{-1+x^3} \, dx\) [120]
3.2.21
\(\int \genfrac {}{}{}{}{x^4}{4+5 x^2+x^4} \, dx\) [121]
3.2.22
\(\int \genfrac {}{}{}{}{2+x}{x+x^2} \, dx\) [122]
3.2.23
\(\int \genfrac {}{}{}{}{1}{x (1+x^2)^2} \, dx\) [123]
3.2.24
\(\int \genfrac {}{}{}{}{1}{(1+x) (2+x)^2 (3+x)^3} \, dx\) [124]
3.2.25
\(\int \genfrac {}{}{}{}{x}{(1+x)^2} \, dx\) [125]
3.2.26
\(\int \genfrac {}{}{}{}{1}{-x+x^3} \, dx\) [126]
3.2.27
\(\int \genfrac {}{}{}{}{x^2}{-6+x+x^2} \, dx\) [127]
3.2.28
\(\int \genfrac {}{}{}{}{2+x}{4-4 x+x^2} \, dx\) [128]
3.2.29
\(\int \genfrac {}{}{}{}{1}{(4-4 x+x^2) (5-4 x+x^2)} \, dx\) [129]
3.2.30
\(\int \genfrac {}{}{}{}{-3+x}{2 x+3 x^2+x^3} \, dx\) [130]
3.2.31
\(\int \genfrac {}{}{}{}{1}{(-1+x^2)^2} \, dx\) [131]
3.2.32
\(\int \genfrac {}{}{}{}{1+x}{-1+x^3} \, dx\) [132]
3.2.33
\(\int \genfrac {}{}{}{}{1+x^4}{x (1+x^2)^2} \, dx\) [133]
3.2.34
\(\int \genfrac {}{}{}{}{1}{-2 x^3+x^4} \, dx\) [134]
3.2.35
\(\int \genfrac {}{}{}{}{1-x^3}{x (1+x^2)} \, dx\) [135]
3.2.36
\(\int \genfrac {}{}{}{}{1}{-1+x^4} \, dx\) [136]
3.2.37
\(\int \genfrac {}{}{}{}{1}{1+x^4} \, dx\) [137]
3.2.38
\(\int \genfrac {}{}{}{}{x^2}{(2+2 x+x^2)^2} \, dx\) [138]
3.2.39
\(\int \genfrac {}{}{}{}{-1+4 x^5}{(1+x+x^5)^2} \, dx\) [139]
3.2.40
\(\int \genfrac {}{}{}{}{1}{5-\cos (x)+2 \sin (x)} \, dx\) [140]
3.2.41
\(\int \genfrac {}{}{}{}{1}{1+a \cos (x)} \, dx\) [141]
3.2.42
\(\int \genfrac {}{}{}{}{1}{1+2 \cos (x)} \, dx\) [142]
3.2.43
\(\int \genfrac {}{}{}{}{1}{1+\genfrac {}{}{}{}{\cos (x)}{2}} \, dx\) [143]
3.2.44
\(\int \genfrac {}{}{}{}{\sin ^2(x)}{1+\sin ^2(x)} \, dx\) [144]
3.2.45
\(\int \genfrac {}{}{}{}{1}{b^2 \cos ^2(x)+a^2 \sin ^2(x)} \, dx\) [145]
3.2.46
\(\int \genfrac {}{}{}{}{1}{(b \cos (x)+a \sin (x))^2} \, dx\) [146]
3.2.47
\(\int \genfrac {}{}{}{}{\sin (x)}{1+\cos (x)+\sin (x)} \, dx\) [147]
3.2.48
\(\int \sqrt {3-x^2} \, dx\) [148]
3.2.49
\(\int \genfrac {}{}{}{}{x}{\sqrt {3-x^2}} \, dx\) [149]
3.2.50
\(\int \genfrac {}{}{}{}{\sqrt {3-x^2}}{x} \, dx\) [150]
3.2.51
\(\int \genfrac {}{}{}{}{\sqrt {x+x^2}}{x} \, dx\) [151]
3.2.52
\(\int \sqrt {5+x^2} \, dx\) [152]
3.2.53
\(\int \genfrac {}{}{}{}{x}{\sqrt {1+x+x^2}} \, dx\) [153]
3.2.54
\(\int \genfrac {}{}{}{}{1}{\sqrt {x+x^2}} \, dx\) [154]
3.2.55
\(\int \genfrac {}{}{}{}{\sqrt {2-x-x^2}}{x^2} \, dx\) [155]
3.2.56
\(\int \genfrac {}{}{}{}{\log (t)}{1+t} \, dt\) [156]
3.2.57
\(\int \log (e^{\cos (x)}) \, dx\) [157]
3.2.58
\(\int \genfrac {}{}{}{}{e^t}{t} \, dt\) [158]
3.2.59
\(\int \genfrac {}{}{}{}{e^{a t}}{t} \, dt\) [159]
3.2.60
\(\int \genfrac {}{}{}{}{e^t}{t^2} \, dt\) [160]
3.2.61
\(\int e^{\genfrac {}{}{}{}{1}{t}} \, dt\) [161]
3.2.62
\(\int \genfrac {}{}{}{}{e^{-t}}{-1-a+t} \, dt\) [162]
3.2.63
\(\int \genfrac {}{}{}{}{e^{t^2} t}{1+t^2} \, dt\) [163]
3.2.64
\(\int \genfrac {}{}{}{}{e^t}{(1+t)^2} \, dt\) [164]
3.2.65
\(\int e^t \log (1+t) \, dt\) [165]
3.2.66
\(\int e^{-t} t \, dt\) [166]
3.2.67
\(\int e^{-t} t^2 \, dt\) [167]
3.2.68
\(\int e^{-t} t^3 \, dt\) [168]
3.2.69
\(\int \genfrac {}{}{}{}{\text {b1} \cos (x)+\text {a1} \sin (x)}{b \cos (x)+a \sin (x)} \, dx\) [169]
3.2.70
\(\int \genfrac {}{}{}{}{1}{\log (t)} \, dt\) [170]
3.2.71
\(\int \genfrac {}{}{}{}{1}{\log ^2(t)} \, dt\) [171]
3.2.72
\(\int \log ^{-1-n}(t) \, dt\) [172]
3.2.73
\(\int \genfrac {}{}{}{}{e^{2 t}}{-1+t} \, dt\) [173]
3.2.74
\(\int \genfrac {}{}{}{}{e^{2 x}}{2-3 x+x^2} \, dx\) [174]
3.2.75
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+t^3}} \, dt\) [175]
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