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Chapter 3
Listing of integrals
3.1
\(\int \sin ^3(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.2
\(\int \sin ^2(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.3
\(\int \sin (e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.4
\(\int (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.5
\(\int \csc (e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.6
\(\int \csc ^2(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.7
\(\int \csc ^3(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.8
\(\int \csc ^4(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.9
\(\int \csc ^5(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.10
\(\int \csc ^6(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.11
\(\int \csc ^7(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\)
3.12
\(\int \sin ^2(c+d x) (a+a \sin (c+d x))^{3/2} (c-c \sin (c+d x)) \, dx\)
3.13
\(\int \frac{\csc (e+f x) \sqrt{a+a \sin (e+f x)}}{c-c \sin (e+f x)} \, dx\)
3.14
\(\int \frac{\csc (e+f x)}{\sqrt{a+a \sin (e+f x)} (c-c \sin (e+f x))} \, dx\)
3.15
\(\int \frac{\sqrt{g \sin (e+f x)} \sqrt{a+a \sin (e+f x)}}{c-c \sin (e+f x)} \, dx\)
3.16
\(\int \frac{\sqrt{a+a \sin (e+f x)}}{\sqrt{g \sin (e+f x)} (c-c \sin (e+f x))} \, dx\)
3.17
\(\int \frac{\sqrt{g \sin (e+f x)}}{\sqrt{a+a \sin (e+f x)} (c-c \sin (e+f x))} \, dx\)
3.18
\(\int \frac{1}{\sqrt{g \sin (e+f x)} \sqrt{a+a \sin (e+f x)} (c-c \sin (e+f x))} \, dx\)
3.19
\(\int \csc (e+f x) \sqrt{a+a \sin (e+f x)} \sqrt{c-c \sin (e+f x)} \, dx\)
3.20
\(\int \frac{\csc (e+f x) \sqrt{a+a \sin (e+f x)}}{\sqrt{c-c \sin (e+f x)}} \, dx\)
3.21
\(\int \frac{\csc (e+f x) \sqrt{c-c \sin (e+f x)}}{\sqrt{a+a \sin (e+f x)}} \, dx\)
3.22
\(\int \frac{\csc (e+f x)}{\sqrt{a+a \sin (e+f x)} \sqrt{c-c \sin (e+f x)}} \, dx\)
3.23
\(\int \frac{\csc (e+f x) \sqrt{a+a \sin (e+f x)}}{c+d \sin (e+f x)} \, dx\)
3.24
\(\int \frac{\csc (e+f x)}{\sqrt{a+a \sin (e+f x)} (c+d \sin (e+f x))} \, dx\)
3.25
\(\int \frac{\sqrt{g \sin (e+f x)} \sqrt{a+a \sin (e+f x)}}{c+d \sin (e+f x)} \, dx\)
3.26
\(\int \frac{\sqrt{a+a \sin (e+f x)}}{\sqrt{g \sin (e+f x)} (c+d \sin (e+f x))} \, dx\)
3.27
\(\int \frac{\sqrt{g \sin (e+f x)}}{\sqrt{a+a \sin (e+f x)} (c+d \sin (e+f x))} \, dx\)
3.28
\(\int \frac{1}{\sqrt{g \sin (e+f x)} \sqrt{a+a \sin (e+f x)} (c+d \sin (e+f x))} \, dx\)
3.29
\(\int \frac{\csc (e+f x) \sqrt{a+b \sin (e+f x)}}{c+c \sin (e+f x)} \, dx\)
3.30
\(\int \frac{\csc (e+f x)}{\sqrt{a+b \sin (e+f x)} (c+c \sin (e+f x))} \, dx\)
3.31
\(\int \frac{\sqrt{g \sin (e+f x)} \sqrt{a+b \sin (e+f x)}}{c+c \sin (e+f x)} \, dx\)
3.32
\(\int \frac{\sqrt{a+b \sin (e+f x)}}{\sqrt{g \sin (e+f x)} (c+c \sin (e+f x))} \, dx\)
3.33
\(\int \frac{\sqrt{g \sin (e+f x)}}{\sqrt{a+b \sin (e+f x)} (c+c \sin (e+f x))} \, dx\)
3.34
\(\int \frac{1}{\sqrt{g \sin (e+f x)} \sqrt{a+b \sin (e+f x)} (c+c \sin (e+f x))} \, dx\)
3.35
\(\int \csc (e+f x) \sqrt{a+a \sin (e+f x)} \sqrt{c+d \sin (e+f x)} \, dx\)
3.36
\(\int \frac{\csc (e+f x) \sqrt{a+a \sin (e+f x)}}{\sqrt{c+d \sin (e+f x)}} \, dx\)
3.37
\(\int \frac{\csc (e+f x) \sqrt{c+d \sin (e+f x)}}{\sqrt{a+a \sin (e+f x)}} \, dx\)
3.38
\(\int \frac{\csc (e+f x)}{\sqrt{a+a \sin (e+f x)} \sqrt{c+d \sin (e+f x)}} \, dx\)
3.39
\(\int \frac{\sin ^2(e+f x)}{(a+b \sin (e+f x))^2 (c+d \sin (e+f x))} \, dx\)
3.40
\(\int \frac{\csc (e+f x) \sqrt{c+d \sin (e+f x)}}{a+b \sin (e+f x)} \, dx\)
3.41
\(\int \frac{\csc (e+f x)}{(a+b \sin (e+f x)) \sqrt{c+d \sin (e+f x)}} \, dx\)
3.42
\(\int \frac{\sqrt{g \sin (e+f x)} \sqrt{a+b \sin (e+f x)}}{c+d \sin (e+f x)} \, dx\)
3.43
\(\int \frac{\sqrt{a+b \sin (e+f x)}}{\sqrt{g \sin (e+f x)} (c+d \sin (e+f x))} \, dx\)
3.44
\(\int \frac{\sqrt{g \sin (e+f x)}}{\sqrt{a+b \sin (e+f x)} (c+d \sin (e+f x))} \, dx\)
3.45
\(\int \frac{1}{\sqrt{g \sin (e+f x)} \sqrt{a+b \sin (e+f x)} (c+d \sin (e+f x))} \, dx\)
3.46
\(\int \frac{\sqrt{g \sin (e+f x)} \sqrt{c+d \sin (e+f x)}}{a+b \sin (e+f x)} \, dx\)
3.47
\(\int \frac{\sqrt{g \sin (e+f x)}}{(a+b \sin (e+f x)) \sqrt{c+d \sin (e+f x)}} \, dx\)
3.48
\(\int \csc (e+f x) \sqrt{a+b \sin (e+f x)} \sqrt{c+d \sin (e+f x)} \, dx\)
3.49
\(\int \frac{\csc (e+f x) \sqrt{a+b \sin (e+f x)}}{\sqrt{c+d \sin (e+f x)}} \, dx\)
3.50
\(\int \frac{\csc (e+f x)}{\sqrt{a+b \sin (e+f x)} \sqrt{c+d \sin (e+f x)}} \, dx\)
3.51
\(\int (a+a \sin (e+f x))^m (A+B \sin (e+f x))^p (c-c \sin (e+f x))^n \, dx\)
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