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