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Chapter 3
Listing of integrals
3.1
\(\int (d+e x)^4 (a+b \tanh ^{-1}(c x)) \, dx\)
3.2
\(\int (d+e x)^3 (a+b \tanh ^{-1}(c x)) \, dx\)
3.3
\(\int (d+e x)^2 (a+b \tanh ^{-1}(c x)) \, dx\)
3.4
\(\int (d+e x) (a+b \tanh ^{-1}(c x)) \, dx\)
3.5
\(\int \frac {a+b \tanh ^{-1}(c x)}{d+e x} \, dx\)
3.6
\(\int \frac {a+b \tanh ^{-1}(c x)}{(d+e x)^2} \, dx\)
3.7
\(\int \frac {a+b \tanh ^{-1}(c x)}{(d+e x)^3} \, dx\)
3.8
\(\int \frac {a+b \tanh ^{-1}(c x)}{(d+e x)^4} \, dx\)
3.9
\(\int (d+e x)^3 (a+b \tanh ^{-1}(c x))^2 \, dx\)
3.10
\(\int (d+e x)^2 (a+b \tanh ^{-1}(c x))^2 \, dx\)
3.11
\(\int (d+e x) (a+b \tanh ^{-1}(c x))^2 \, dx\)
3.12
\(\int \frac {(a+b \tanh ^{-1}(c x))^2}{d+e x} \, dx\)
3.13
\(\int \frac {(a+b \tanh ^{-1}(c x))^2}{(d+e x)^2} \, dx\)
3.14
\(\int \frac {(a+b \tanh ^{-1}(c x))^2}{(d+e x)^3} \, dx\)
3.15
\(\int (d+e x)^3 (a+b \tanh ^{-1}(c x))^3 \, dx\)
3.16
\(\int (d+e x)^2 (a+b \tanh ^{-1}(c x))^3 \, dx\)
3.17
\(\int (d+e x) (a+b \tanh ^{-1}(c x))^3 \, dx\)
3.18
\(\int \frac {(a+b \tanh ^{-1}(c x))^3}{d+e x} \, dx\)
3.19
\(\int \frac {(a+b \tanh ^{-1}(c x))^3}{(d+e x)^2} \, dx\)
3.20
\(\int \frac {(a+b \tanh ^{-1}(c x))^3}{(d+e x)^3} \, dx\)
3.21
\(\int \frac {a+b \tanh ^{-1}(c x)}{1+2 c x} \, dx\)
3.22
\(\int \frac {\tanh ^{-1}(x)}{1-\sqrt {2} x} \, dx\)
3.23
\(\int (d+e x)^3 (a+b \tanh ^{-1}(c x^2)) \, dx\)
3.24
\(\int (d+e x)^2 (a+b \tanh ^{-1}(c x^2)) \, dx\)
3.25
\(\int (d+e x) (a+b \tanh ^{-1}(c x^2)) \, dx\)
3.26
\(\int \frac {a+b \tanh ^{-1}(c x^2)}{d+e x} \, dx\)
3.27
\(\int \frac {a+b \tanh ^{-1}(c x^2)}{(d+e x)^2} \, dx\)
3.28
\(\int \frac {a+b \tanh ^{-1}(c x^2)}{(d+e x)^3} \, dx\)
3.29
\(\int (d+e x) (a+b \tanh ^{-1}(c x^2))^2 \, dx\)
3.30
\(\int \frac {(a+b \tanh ^{-1}(c x^2))^2}{d+e x} \, dx\)
3.31
\(\int \frac {(a+b \tanh ^{-1}(c x^2))^2}{(d+e x)^2} \, dx\)
3.32
\(\int (d+e x)^2 (a+b \tanh ^{-1}(c x^3)) \, dx\)
3.33
\(\int (d+e x) (a+b \tanh ^{-1}(c x^3)) \, dx\)
3.34
\(\int \frac {a+b \tanh ^{-1}(c x^3)}{d+e x} \, dx\)
3.35
\(\int \frac {a+b \tanh ^{-1}(c x^3)}{(d+e x)^2} \, dx\)
3.36
\(\int \frac {x^3 (a+b \tanh ^{-1}(c \sqrt {x}))}{1-c^2 x} \, dx\)
3.37
\(\int \frac {x^2 (a+b \tanh ^{-1}(c \sqrt {x}))}{1-c^2 x} \, dx\)
3.38
\(\int \frac {x (a+b \tanh ^{-1}(c \sqrt {x}))}{1-c^2 x} \, dx\)
3.39
\(\int \frac {a+b \tanh ^{-1}(c \sqrt {x})}{1-c^2 x} \, dx\)
3.40
\(\int \frac {a+b \tanh ^{-1}(c \sqrt {x})}{x (1-c^2 x)} \, dx\)
3.41
\(\int \frac {a+b \tanh ^{-1}(c \sqrt {x})}{x^2 (1-c^2 x)} \, dx\)
3.42
\(\int \frac {a+b \tanh ^{-1}(c \sqrt {x})}{x^3 (1-c^2 x)} \, dx\)
3.43
\(\int \frac {a+b \tanh ^{-1}(c \sqrt {x})}{x^4 (1-c^2 x)} \, dx\)
3.44
\(\int \frac {x^2 (a+b \tanh ^{-1}(c \sqrt {x}))}{d+e x} \, dx\)
3.45
\(\int \frac {x (a+b \tanh ^{-1}(c \sqrt {x}))}{d+e x} \, dx\)
3.46
\(\int \frac {a+b \tanh ^{-1}(c \sqrt {x})}{d+e x} \, dx\)
3.47
\(\int \frac {a+b \tanh ^{-1}(c \sqrt {x})}{x (d+e x)} \, dx\)
3.48
\(\int \frac {a+b \tanh ^{-1}(c \sqrt {x})}{x^2 (d+e x)} \, dx\)
3.49
\(\int \frac {a+b \tanh ^{-1}(c \sqrt {x})}{x^3 (d+e x)} \, dx\)
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