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Chapter 3
Listing of integrals
3.1
\(\int x^3 \tanh ^{-1}(a+b x)^2 \, dx\)
3.2
\(\int x^2 \tanh ^{-1}(a+b x)^2 \, dx\)
3.3
\(\int x \tanh ^{-1}(a+b x)^2 \, dx\)
3.4
\(\int \tanh ^{-1}(a+b x)^2 \, dx\)
3.5
\(\int \frac{\tanh ^{-1}(a+b x)^2}{x} \, dx\)
3.6
\(\int \frac{\tanh ^{-1}(a+b x)^2}{x^2} \, dx\)
3.7
\(\int \frac{\tanh ^{-1}(a+b x)^2}{x^3} \, dx\)
3.8
\(\int \frac{\tanh ^{-1}(1+b x)^2}{x} \, dx\)
3.9
\(\int (c e+d e x)^3 (a+b \tanh ^{-1}(c+d x)) \, dx\)
3.10
\(\int (c e+d e x)^2 (a+b \tanh ^{-1}(c+d x)) \, dx\)
3.11
\(\int (c e+d e x) (a+b \tanh ^{-1}(c+d x)) \, dx\)
3.12
\(\int \frac{a+b \tanh ^{-1}(c+d x)}{c e+d e x} \, dx\)
3.13
\(\int \frac{a+b \tanh ^{-1}(c+d x)}{(c e+d e x)^2} \, dx\)
3.14
\(\int \frac{a+b \tanh ^{-1}(c+d x)}{(c e+d e x)^3} \, dx\)
3.15
\(\int (c e+d e x)^3 (a+b \tanh ^{-1}(c+d x))^2 \, dx\)
3.16
\(\int (c e+d e x)^2 (a+b \tanh ^{-1}(c+d x))^2 \, dx\)
3.17
\(\int (c e+d e x) (a+b \tanh ^{-1}(c+d x))^2 \, dx\)
3.18
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^2}{c e+d e x} \, dx\)
3.19
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^2}{(c e+d e x)^2} \, dx\)
3.20
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^2}{(c e+d e x)^3} \, dx\)
3.21
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^2}{(c e+d e x)^4} \, dx\)
3.22
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^2}{(c e+d e x)^5} \, dx\)
3.23
\(\int (c e+d e x)^2 (a+b \tanh ^{-1}(c+d x))^3 \, dx\)
3.24
\(\int (c e+d e x) (a+b \tanh ^{-1}(c+d x))^3 \, dx\)
3.25
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^3}{c e+d e x} \, dx\)
3.26
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^3}{(c e+d e x)^2} \, dx\)
3.27
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^3}{(c e+d e x)^3} \, dx\)
3.28
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^3}{(c e+d e x)^4} \, dx\)
3.29
\(\int \frac{\tanh ^{-1}(1+x)}{2+2 x} \, dx\)
3.30
\(\int \frac{\tanh ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx\)
3.31
\(\int (e+f x)^3 (a+b \tanh ^{-1}(c+d x)) \, dx\)
3.32
\(\int (e+f x)^2 (a+b \tanh ^{-1}(c+d x)) \, dx\)
3.33
\(\int (e+f x) (a+b \tanh ^{-1}(c+d x)) \, dx\)
3.34
\(\int (a+b \tanh ^{-1}(c+d x)) \, dx\)
3.35
\(\int \frac{a+b \tanh ^{-1}(c+d x)}{e+f x} \, dx\)
3.36
\(\int \frac{a+b \tanh ^{-1}(c+d x)}{(e+f x)^2} \, dx\)
3.37
\(\int \frac{a+b \tanh ^{-1}(c+d x)}{(e+f x)^3} \, dx\)
3.38
\(\int (e+f x)^3 (a+b \tanh ^{-1}(c+d x))^2 \, dx\)
3.39
\(\int (e+f x)^2 (a+b \tanh ^{-1}(c+d x))^2 \, dx\)
3.40
\(\int (e+f x) (a+b \tanh ^{-1}(c+d x))^2 \, dx\)
3.41
\(\int (a+b \tanh ^{-1}(c+d x))^2 \, dx\)
3.42
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^2}{e+f x} \, dx\)
3.43
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^2}{(e+f x)^2} \, dx\)
3.44
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^2}{(e+f x)^3} \, dx\)
3.45
\(\int (e+f x)^2 (a+b \tanh ^{-1}(c+d x))^3 \, dx\)
3.46
\(\int (e+f x) (a+b \tanh ^{-1}(c+d x))^3 \, dx\)
3.47
\(\int (a+b \tanh ^{-1}(c+d x))^3 \, dx\)
3.48
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^3}{e+f x} \, dx\)
3.49
\(\int \frac{(a+b \tanh ^{-1}(c+d x))^3}{(e+f x)^2} \, dx\)
3.50
\(\int (e+f x)^m (a+b \tanh ^{-1}(c+d x))^3 \, dx\)
3.51
\(\int (e+f x)^m (a+b \tanh ^{-1}(c+d x))^2 \, dx\)
3.52
\(\int (e+f x)^m (a+b \tanh ^{-1}(c+d x)) \, dx\)
3.53
\(\int \frac{\tanh ^{-1}(a+b x)}{c+d x^3} \, dx\)
3.54
\(\int \frac{\tanh ^{-1}(a+b x)}{c+d x^2} \, dx\)
3.55
\(\int \frac{\tanh ^{-1}(a+b x)}{c+d x} \, dx\)
3.56
\(\int \frac{\tanh ^{-1}(a+b x)}{c+\frac{d}{x}} \, dx\)
3.57
\(\int \frac{\tanh ^{-1}(a+b x)}{c+\frac{d}{x^2}} \, dx\)
3.58
\(\int \frac{\tanh ^{-1}(a+b x)}{c+\frac{d}{x^3}} \, dx\)
3.59
\(\int \frac{\tanh ^{-1}(a+b x)}{c+d \sqrt{x}} \, dx\)
3.60
\(\int \frac{\tanh ^{-1}(a+b x)}{c+\frac{d}{\sqrt{x}}} \, dx\)
3.61
\(\int \frac{\tanh ^{-1}(d+e x)}{a+b x+c x^2} \, dx\)
3.62
\(\int \frac{(c e+d e x) (a+b \tanh ^{-1}(c+d x))}{1-(c+d x)^2} \, dx\)
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