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Chapter 3
Listing of integrals
3.1
\(\int \frac{\sin ^4(x)}{a+a \cos (x)} \, dx\)
3.2
\(\int \frac{\sin ^3(x)}{a+a \cos (x)} \, dx\)
3.3
\(\int \frac{\sin ^2(x)}{a+a \cos (x)} \, dx\)
3.4
\(\int \frac{\sin (x)}{a+a \cos (x)} \, dx\)
3.5
\(\int \frac{1}{a+a \cos (x)} \, dx\)
3.6
\(\int \frac{\csc (x)}{a+a \cos (x)} \, dx\)
3.7
\(\int \frac{\csc ^2(x)}{a+a \cos (x)} \, dx\)
3.8
\(\int \frac{\csc ^3(x)}{a+a \cos (x)} \, dx\)
3.9
\(\int \frac{\csc ^4(x)}{a+a \cos (x)} \, dx\)
3.10
\(\int \frac{\sin (2 x)}{1+\cos (2 x)} \, dx\)
3.11
\(\int \frac{\sin (2 x)}{1-\cos (2 x)} \, dx\)
3.12
\(\int \frac{\sin (x)}{(1+\cos (x))^2} \, dx\)
3.13
\(\int \frac{\sin (x)}{(1-\cos (x))^2} \, dx\)
3.14
\(\int \frac{\sin ^2(x)}{(1+\cos (x))^2} \, dx\)
3.15
\(\int \frac{\sin ^2(x)}{(1-\cos (x))^2} \, dx\)
3.16
\(\int \frac{\sin ^3(x)}{(1+\cos (x))^2} \, dx\)
3.17
\(\int \frac{\sin ^3(x)}{(1-\cos (x))^2} \, dx\)
3.18
\(\int \frac{\sin (x)}{(1+\cos (x))^3} \, dx\)
3.19
\(\int \frac{\sin (x)}{(1-\cos (x))^3} \, dx\)
3.20
\(\int \frac{\sin ^2(x)}{(1+\cos (x))^3} \, dx\)
3.21
\(\int \frac{\sin ^2(x)}{(1-\cos (x))^3} \, dx\)
3.22
\(\int \frac{\sin ^3(x)}{(1+\cos (x))^3} \, dx\)
3.23
\(\int \frac{\sin ^3(x)}{(1-\cos (x))^3} \, dx\)
3.24
\(\int \frac{\sin ^4(x)}{a+b \cos (x)} \, dx\)
3.25
\(\int \frac{\sin ^3(x)}{a+b \cos (x)} \, dx\)
3.26
\(\int \frac{\sin ^2(x)}{a+b \cos (x)} \, dx\)
3.27
\(\int \frac{\sin (x)}{a+b \cos (x)} \, dx\)
3.28
\(\int \frac{1}{a+b \cos (x)} \, dx\)
3.29
\(\int \frac{\csc (x)}{a+b \cos (x)} \, dx\)
3.30
\(\int \frac{\csc ^2(x)}{a+b \cos (x)} \, dx\)
3.31
\(\int \frac{\csc ^3(x)}{a+b \cos (x)} \, dx\)
3.32
\(\int \frac{\csc ^4(x)}{a+b \cos (x)} \, dx\)
3.33
\(\int (a+b \cos (c+d x)) (e \sin (c+d x))^{7/2} \, dx\)
3.34
\(\int (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2} \, dx\)
3.35
\(\int (a+b \cos (c+d x)) (e \sin (c+d x))^{3/2} \, dx\)
3.36
\(\int (a+b \cos (c+d x)) \sqrt{e \sin (c+d x)} \, dx\)
3.37
\(\int \frac{a+b \cos (c+d x)}{\sqrt{e \sin (c+d x)}} \, dx\)
3.38
\(\int \frac{a+b \cos (c+d x)}{(e \sin (c+d x))^{3/2}} \, dx\)
3.39
\(\int \frac{a+b \cos (c+d x)}{(e \sin (c+d x))^{5/2}} \, dx\)
3.40
\(\int \frac{a+b \cos (c+d x)}{(e \sin (c+d x))^{7/2}} \, dx\)
3.41
\(\int (a+b \cos (c+d x))^2 (e \sin (c+d x))^{7/2} \, dx\)
3.42
\(\int (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2} \, dx\)
3.43
\(\int (a+b \cos (c+d x))^2 (e \sin (c+d x))^{3/2} \, dx\)
3.44
\(\int (a+b \cos (c+d x))^2 \sqrt{e \sin (c+d x)} \, dx\)
3.45
\(\int \frac{(a+b \cos (c+d x))^2}{\sqrt{e \sin (c+d x)}} \, dx\)
3.46
\(\int \frac{(a+b \cos (c+d x))^2}{(e \sin (c+d x))^{3/2}} \, dx\)
3.47
\(\int \frac{(a+b \cos (c+d x))^2}{(e \sin (c+d x))^{5/2}} \, dx\)
3.48
\(\int \frac{(a+b \cos (c+d x))^2}{(e \sin (c+d x))^{7/2}} \, dx\)
3.49
\(\int (a+b \cos (c+d x))^3 (e \sin (c+d x))^{7/2} \, dx\)
3.50
\(\int (a+b \cos (c+d x))^3 (e \sin (c+d x))^{5/2} \, dx\)
3.51
\(\int (a+b \cos (c+d x))^3 (e \sin (c+d x))^{3/2} \, dx\)
3.52
\(\int (a+b \cos (c+d x))^3 \sqrt{e \sin (c+d x)} \, dx\)
3.53
\(\int \frac{(a+b \cos (c+d x))^3}{\sqrt{e \sin (c+d x)}} \, dx\)
3.54
\(\int \frac{(a+b \cos (c+d x))^3}{(e \sin (c+d x))^{3/2}} \, dx\)
3.55
\(\int \frac{(a+b \cos (c+d x))^3}{(e \sin (c+d x))^{5/2}} \, dx\)
3.56
\(\int \frac{(a+b \cos (c+d x))^3}{(e \sin (c+d x))^{7/2}} \, dx\)
3.57
\(\int \frac{(a+b \cos (c+d x))^3}{(e \sin (c+d x))^{9/2}} \, dx\)
3.58
\(\int \frac{(e \sin (c+d x))^{11/2}}{a+b \cos (c+d x)} \, dx\)
3.59
\(\int \frac{(e \sin (c+d x))^{9/2}}{a+b \cos (c+d x)} \, dx\)
3.60
\(\int \frac{(e \sin (c+d x))^{7/2}}{a+b \cos (c+d x)} \, dx\)
3.61
\(\int \frac{(e \sin (c+d x))^{5/2}}{a+b \cos (c+d x)} \, dx\)
3.62
\(\int \frac{(e \sin (c+d x))^{3/2}}{a+b \cos (c+d x)} \, dx\)
3.63
\(\int \frac{\sqrt{e \sin (c+d x)}}{a+b \cos (c+d x)} \, dx\)
3.64
\(\int \frac{1}{(a+b \cos (c+d x)) \sqrt{e \sin (c+d x)}} \, dx\)
3.65
\(\int \frac{1}{(a+b \cos (c+d x)) (e \sin (c+d x))^{3/2}} \, dx\)
3.66
\(\int \frac{1}{(a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}} \, dx\)
3.67
\(\int \frac{1}{(a+b \cos (c+d x)) (e \sin (c+d x))^{7/2}} \, dx\)
3.68
\(\int \frac{(e \sin (c+d x))^{11/2}}{(a+b \cos (c+d x))^2} \, dx\)
3.69
\(\int \frac{(e \sin (c+d x))^{9/2}}{(a+b \cos (c+d x))^2} \, dx\)
3.70
\(\int \frac{(e \sin (c+d x))^{7/2}}{(a+b \cos (c+d x))^2} \, dx\)
3.71
\(\int \frac{(e \sin (c+d x))^{5/2}}{(a+b \cos (c+d x))^2} \, dx\)
3.72
\(\int \frac{(e \sin (c+d x))^{3/2}}{(a+b \cos (c+d x))^2} \, dx\)
3.73
\(\int \frac{\sqrt{e \sin (c+d x)}}{(a+b \cos (c+d x))^2} \, dx\)
3.74
\(\int \frac{1}{(a+b \cos (c+d x))^2 \sqrt{e \sin (c+d x)}} \, dx\)
3.75
\(\int \frac{1}{(a+b \cos (c+d x))^2 (e \sin (c+d x))^{3/2}} \, dx\)
3.76
\(\int \frac{1}{(a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}} \, dx\)
3.77
\(\int \frac{1}{(a+b \cos (c+d x))^2 (e \sin (c+d x))^{7/2}} \, dx\)
3.78
\(\int \frac{(e \sin (c+d x))^{13/2}}{(a+b \cos (c+d x))^3} \, dx\)
3.79
\(\int \frac{(e \sin (c+d x))^{11/2}}{(a+b \cos (c+d x))^3} \, dx\)
3.80
\(\int \frac{(e \sin (c+d x))^{9/2}}{(a+b \cos (c+d x))^3} \, dx\)
3.81
\(\int \frac{(e \sin (c+d x))^{7/2}}{(a+b \cos (c+d x))^3} \, dx\)
3.82
\(\int \frac{(e \sin (c+d x))^{5/2}}{(a+b \cos (c+d x))^3} \, dx\)
3.83
\(\int \frac{(e \sin (c+d x))^{3/2}}{(a+b \cos (c+d x))^3} \, dx\)
3.84
\(\int \frac{\sqrt{e \sin (c+d x)}}{(a+b \cos (c+d x))^3} \, dx\)
3.85
\(\int \frac{1}{(a+b \cos (c+d x))^3 \sqrt{e \sin (c+d x)}} \, dx\)
3.86
\(\int \frac{1}{(a+b \cos (c+d x))^3 (e \sin (c+d x))^{3/2}} \, dx\)
3.87
\(\int \frac{1}{(a+b \cos (c+d x))^3 (e \sin (c+d x))^{5/2}} \, dx\)
3.88
\(\int \frac{1}{(a+b \cos (c+d x))^3 (e \sin (c+d x))^{7/2}} \, dx\)
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