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Chapter 3
Listing of integrals
3.1
\(\int \frac{\sin ^6(x)}{a-a \cos ^2(x)} \, dx\)
3.2
\(\int \frac{\sin ^5(x)}{a-a \cos ^2(x)} \, dx\)
3.3
\(\int \frac{\sin ^4(x)}{a-a \cos ^2(x)} \, dx\)
3.4
\(\int \frac{\sin ^3(x)}{a-a \cos ^2(x)} \, dx\)
3.5
\(\int \frac{\sin ^2(x)}{a-a \cos ^2(x)} \, dx\)
3.6
\(\int \frac{\sin (x)}{a-a \cos ^2(x)} \, dx\)
3.7
\(\int \frac{\csc (x)}{a-a \cos ^2(x)} \, dx\)
3.8
\(\int \frac{\csc ^2(x)}{a-a \cos ^2(x)} \, dx\)
3.9
\(\int \frac{\csc ^3(x)}{a-a \cos ^2(x)} \, dx\)
3.10
\(\int \frac{\sin ^7(x)}{a+b \cos ^2(x)} \, dx\)
3.11
\(\int \frac{\sin ^5(x)}{a+b \cos ^2(x)} \, dx\)
3.12
\(\int \frac{\sin ^3(x)}{a+b \cos ^2(x)} \, dx\)
3.13
\(\int \frac{\sin (x)}{a+b \cos ^2(x)} \, dx\)
3.14
\(\int \frac{\csc (x)}{a+b \cos ^2(x)} \, dx\)
3.15
\(\int \frac{\csc ^3(x)}{a+b \cos ^2(x)} \, dx\)
3.16
\(\int \frac{\csc ^5(x)}{a+b \cos ^2(x)} \, dx\)
3.17
\(\int \frac{\sin ^6(x)}{a+b \cos ^2(x)} \, dx\)
3.18
\(\int \frac{\sin ^4(x)}{a+b \cos ^2(x)} \, dx\)
3.19
\(\int \frac{\sin ^2(x)}{a+b \cos ^2(x)} \, dx\)
3.20
\(\int \frac{1}{a+b \cos ^2(x)} \, dx\)
3.21
\(\int \frac{\csc ^2(x)}{a+b \cos ^2(x)} \, dx\)
3.22
\(\int \frac{\csc ^4(x)}{a+b \cos ^2(x)} \, dx\)
3.23
\(\int \frac{\csc ^6(x)}{a+b \cos ^2(x)} \, dx\)
3.24
\(\int \frac{\sin (x)}{4-3 \cos ^3(x)} \, dx\)
3.25
\(\int \frac{1}{1-\cos ^2(x)} \, dx\)
3.26
\(\int \frac{1}{(1-\cos ^2(x))^2} \, dx\)
3.27
\(\int \frac{1}{(1-\cos ^2(x))^3} \, dx\)
3.28
\(\int \frac{\cos ^7(x)}{a+b \cos ^2(x)} \, dx\)
3.29
\(\int \frac{\cos ^5(x)}{a+b \cos ^2(x)} \, dx\)
3.30
\(\int \frac{\cos ^3(x)}{a+b \cos ^2(x)} \, dx\)
3.31
\(\int \frac{\cos (x)}{a+b \cos ^2(x)} \, dx\)
3.32
\(\int \frac{\sec (x)}{a+b \cos ^2(x)} \, dx\)
3.33
\(\int \frac{\sec ^3(x)}{a+b \cos ^2(x)} \, dx\)
3.34
\(\int \frac{\sec ^5(x)}{a+b \cos ^2(x)} \, dx\)
3.35
\(\int \frac{\cos ^6(x)}{a+b \cos ^2(x)} \, dx\)
3.36
\(\int \frac{\cos ^4(x)}{a+b \cos ^2(x)} \, dx\)
3.37
\(\int \frac{\cos ^2(x)}{a+b \cos ^2(x)} \, dx\)
3.38
\(\int \frac{1}{a+b \cos ^2(x)} \, dx\)
3.39
\(\int \frac{\sec ^2(x)}{a+b \cos ^2(x)} \, dx\)
3.40
\(\int \frac{\sec ^4(x)}{a+b \cos ^2(x)} \, dx\)
3.41
\(\int \frac{\sec ^6(x)}{a+b \cos ^2(x)} \, dx\)
3.42
\(\int \frac{1}{(a+b \cos ^2(x))^2} \, dx\)
3.43
\(\int \frac{1}{(a+b \cos ^2(x))^3} \, dx\)
3.44
\(\int \frac{1}{1+\cos ^2(x)} \, dx\)
3.45
\(\int \frac{1}{(1+\cos ^2(x))^2} \, dx\)
3.46
\(\int \frac{1}{(1+\cos ^2(x))^3} \, dx\)
3.47
\(\int \sqrt{1-\cos ^2(x)} \, dx\)
3.48
\(\int \sqrt{-1+\cos ^2(x)} \, dx\)
3.49
\(\int (1-\cos ^2(x))^{3/2} \, dx\)
3.50
\(\int (-1+\cos ^2(x))^{3/2} \, dx\)
3.51
\(\int \frac{1}{\sqrt{1-\cos ^2(x)}} \, dx\)
3.52
\(\int \frac{1}{\sqrt{-1+\cos ^2(x)}} \, dx\)
3.53
\(\int \frac{1}{(1-\cos ^2(x))^{3/2}} \, dx\)
3.54
\(\int \frac{1}{(-1+\cos ^2(x))^{3/2}} \, dx\)
3.55
\(\int \sqrt{1+\cos ^2(x)} \, dx\)
3.56
\(\int \sqrt{-1-\cos ^2(x)} \, dx\)
3.57
\(\int \sqrt{a+b \cos ^2(x)} \, dx\)
3.58
\(\int (1+\cos ^2(x))^{3/2} \, dx\)
3.59
\(\int (-1-\cos ^2(x))^{3/2} \, dx\)
3.60
\(\int (a+b \cos ^2(x))^{3/2} \, dx\)
3.61
\(\int \frac{1}{\sqrt{1+\cos ^2(x)}} \, dx\)
3.62
\(\int \frac{1}{\sqrt{-1-\cos ^2(x)}} \, dx\)
3.63
\(\int \frac{1}{\sqrt{a+b \cos ^2(x)}} \, dx\)
3.64
\(\int \frac{1}{(1+\cos ^2(x))^{3/2}} \, dx\)
3.65
\(\int \frac{1}{(-1-\cos ^2(x))^{3/2}} \, dx\)
3.66
\(\int \frac{1}{(a+b \cos ^2(x))^{3/2}} \, dx\)
3.67
\(\int \frac{\cos (x)}{\sqrt{1+\cos ^2(x)}} \, dx\)
3.68
\(\int \frac{\cos (5+3 x)}{\sqrt{3+\cos ^2(5+3 x)}} \, dx\)
3.69
\(\int \frac{\cos (x)}{\sqrt{4-\cos ^2(x)}} \, dx\)
3.70
\(\int \frac{1}{a+b \cos ^4(x)} \, dx\)
3.71
\(\int \frac{1}{a-b \cos ^4(x)} \, dx\)
3.72
\(\int \frac{1}{1+\cos ^4(x)} \, dx\)
3.73
\(\int \frac{1}{1-\cos ^4(x)} \, dx\)
3.74
\(\int \frac{1}{a+b \cos ^5(x)} \, dx\)
3.75
\(\int \frac{1}{a+b \cos ^6(x)} \, dx\)
3.76
\(\int \frac{1}{a+b \cos ^8(x)} \, dx\)
3.77
\(\int \frac{1}{a-b \cos ^5(x)} \, dx\)
3.78
\(\int \frac{1}{a-b \cos ^6(x)} \, dx\)
3.79
\(\int \frac{1}{a-b \cos ^8(x)} \, dx\)
3.80
\(\int \frac{1}{1+\cos ^5(x)} \, dx\)
3.81
\(\int \frac{1}{1+\cos ^6(x)} \, dx\)
3.82
\(\int \frac{1}{1+\cos ^8(x)} \, dx\)
3.83
\(\int \frac{1}{1-\cos ^5(x)} \, dx\)
3.84
\(\int \frac{1}{1-\cos ^6(x)} \, dx\)
3.85
\(\int \frac{1}{1-\cos ^8(x)} \, dx\)
3.86
\(\int \frac{\tan (x)}{1+\cos ^2(x)} \, dx\)
3.87
\(\int \sqrt{a+b \cos ^2(x)} \tan (x) \, dx\)
3.88
\(\int \sqrt{1-\cos ^2(x)} \tan (x) \, dx\)
3.89
\(\int \frac{\tan (x)}{\sqrt{a+b \cos ^2(x)}} \, dx\)
3.90
\(\int \frac{\tan (x)}{\sqrt{1+\cos ^2(x)}} \, dx\)
3.91
\(\int \frac{\tan (x)}{\sqrt{1-\cos ^2(x)}} \, dx\)
3.92
\(\int \frac{\tan ^3(x)}{a+b \cos ^3(x)} \, dx\)
3.93
\(\int \sqrt{a+b \cos ^3(x)} \tan (x) \, dx\)
3.94
\(\int \frac{\tan (x)}{\sqrt{a+b \cos ^3(x)}} \, dx\)
3.95
\(\int \sqrt{a+b \cos ^4(x)} \tan (x) \, dx\)
3.96
\(\int \frac{\tan (x)}{\sqrt{a+b \cos ^4(x)}} \, dx\)
3.97
\(\int \sqrt{a+b \cos ^n(x)} \tan (x) \, dx\)
3.98
\(\int \frac{\tan (x)}{\sqrt{a+b \cos ^n(x)}} \, dx\)
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