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3
Listing of integrals
3.1
\(\int x^2 \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right ) \, dx\)
3.2
\(\int x \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right ) \, dx\)
3.3
\(\int \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right ) \, dx\)
3.4
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x} \, dx\)
3.5
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x^2} \, dx\)
3.6
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x^3} \, dx\)
3.7
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x^4} \, dx\)
3.8
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x^5} \, dx\)
3.9
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x^6} \, dx\)
3.10
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x^7} \, dx\)
3.11
\(\int x^2 \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2 \, dx\)
3.12
\(\int x \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2 \, dx\)
3.13
\(\int \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2 \, dx\)
3.14
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2}{x} \, dx\)
3.15
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2}{x^2} \, dx\)
3.16
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2}{x^3} \, dx\)
3.17
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2}{x^4} \, dx\)
3.18
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2}{x^5} \, dx\)
3.19
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2}{x^6} \, dx\)
3.20
\(\int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2}{x^7} \, dx\)
3.21
\(\int \frac{x^4 \left (A+B x+C x^2\right )}{a+b x^2+c x^4} \, dx\)
3.22
\(\int \frac{x^3 \left (A+B x+C x^2\right )}{a+b x^2+c x^4} \, dx\)
3.23
\(\int \frac{x^2 \left (A+B x+C x^2\right )}{a+b x^2+c x^4} \, dx\)
3.24
\(\int \frac{x \left (A+B x+C x^2\right )}{a+b x^2+c x^4} \, dx\)
3.25
\(\int \frac{A+B x+C x^2}{a+b x^2+c x^4} \, dx\)
3.26
\(\int \frac{A+B x+C x^2}{x \left (a+b x^2+c x^4\right )} \, dx\)
3.27
\(\int \frac{A+B x+C x^2}{x^2 \left (a+b x^2+c x^4\right )} \, dx\)
3.28
\(\int \frac{A+B x+C x^2}{x^3 \left (a+b x^2+c x^4\right )} \, dx\)
3.29
\(\int \frac{x^4 \left (A+B x+C x^2\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.30
\(\int \frac{x^3 \left (A+B x+C x^2\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.31
\(\int \frac{x^2 \left (A+B x+C x^2\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.32
\(\int \frac{x \left (A+B x+C x^2\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.33
\(\int \frac{A+B x+C x^2}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.34
\(\int \frac{A+B x+C x^2}{x \left (a+b x^2+c x^4\right )^2} \, dx\)
3.35
\(\int \frac{A+B x+C x^2}{x^2 \left (a+b x^2+c x^4\right )^2} \, dx\)
3.36
\(\int \frac{A+B x+C x^2}{x^3 \left (a+b x^2+c x^4\right )^2} \, dx\)
3.37
\(\int (d x)^m \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^3 \, dx\)
3.38
\(\int (d x)^m \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2 \, dx\)
3.39
\(\int (d x)^m \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right ) \, dx\)
3.40
\(\int \frac{(d x)^m \left (A+B x+C x^2\right )}{a+b x^2+c x^4} \, dx\)
3.41
\(\int \frac{(d x)^m \left (A+B x+C x^2\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.42
\(\int \frac{x^2 \left (A+B x+C x^2\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.43
\(\int \frac{x \left (A x+B x^2+C x^3\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.44
\(\int \frac{A x^2+B x^3+C x^4}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.45
\(\int \frac{A x^3+B x^4+C x^5}{x \left (a+b x^2+c x^4\right )^2} \, dx\)
3.46
\(\int \frac{A x^4+B x^5+C x^6}{x^2 \left (a+b x^2+c x^4\right )^2} \, dx\)
3.47
\(\int \frac{x^7 \left (d+e x^2+f x^4\right )}{a+b x^2+c x^4} \, dx\)
3.48
\(\int \frac{x^5 \left (d+e x^2+f x^4\right )}{a+b x^2+c x^4} \, dx\)
3.49
\(\int \frac{x^3 \left (d+e x^2+f x^4\right )}{a+b x^2+c x^4} \, dx\)
3.50
\(\int \frac{x \left (d+e x^2+f x^4\right )}{a+b x^2+c x^4} \, dx\)
3.51
\(\int \frac{d+e x^2+f x^4}{x \left (a+b x^2+c x^4\right )} \, dx\)
3.52
\(\int \frac{d+e x^2+f x^4}{x^3 \left (a+b x^2+c x^4\right )} \, dx\)
3.53
\(\int \frac{d+e x^2+f x^4}{x^5 \left (a+b x^2+c x^4\right )} \, dx\)
3.54
\(\int \frac{d+e x^2+f x^4}{x^7 \left (a+b x^2+c x^4\right )} \, dx\)
3.55
\(\int \frac{x^4 \left (d+e x^2+f x^4\right )}{a+b x^2+c x^4} \, dx\)
3.56
\(\int \frac{x^2 \left (d+e x^2+f x^4\right )}{a+b x^2+c x^4} \, dx\)
3.57
\(\int \frac{d+e x^2+f x^4}{a+b x^2+c x^4} \, dx\)
3.58
\(\int \frac{d+e x^2+f x^4}{x^2 \left (a+b x^2+c x^4\right )} \, dx\)
3.59
\(\int \frac{d+e x^2+f x^4}{x^4 \left (a+b x^2+c x^4\right )} \, dx\)
3.60
\(\int \frac{d+e x^2+f x^4}{x^6 \left (a+b x^2+c x^4\right )} \, dx\)
3.61
\(\int \frac{x^7 \left (d+e x^2+f x^4\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.62
\(\int \frac{x^5 \left (d+e x^2+f x^4\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.63
\(\int \frac{x^3 \left (d+e x^2+f x^4\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.64
\(\int \frac{x \left (d+e x^2+f x^4\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.65
\(\int \frac{d+e x^2+f x^4}{x \left (a+b x^2+c x^4\right )^2} \, dx\)
3.66
\(\int \frac{d+e x^2+f x^4}{x^3 \left (a+b x^2+c x^4\right )^2} \, dx\)
3.67
\(\int \frac{d+e x^2+f x^4}{x^5 \left (a+b x^2+c x^4\right )^2} \, dx\)
3.68
\(\int \frac{x^6 \left (d+e x^2+f x^4\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.69
\(\int \frac{x^4 \left (d+e x^2+f x^4\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.70
\(\int \frac{x^2 \left (d+e x^2+f x^4\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.71
\(\int \frac{d+e x^2+f x^4}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.72
\(\int \frac{d+e x^2+f x^4}{x^2 \left (a+b x^2+c x^4\right )^2} \, dx\)
3.73
\(\int \frac{d+e x^2+f x^4}{x^4 \left (a+b x^2+c x^4\right )^2} \, dx\)
3.74
\(\int \frac{x^9 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.75
\(\int \frac{x^7 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.76
\(\int \frac{x^5 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.77
\(\int \frac{x^3 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.78
\(\int \frac{x \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.79
\(\int \frac{4+x^2+3 x^4+5 x^6}{x \left (2+3 x^2+x^4\right )^2} \, dx\)
3.80
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^3 \left (2+3 x^2+x^4\right )^2} \, dx\)
3.81
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^5 \left (2+3 x^2+x^4\right )^2} \, dx\)
3.82
\(\int \frac{x^8 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.83
\(\int \frac{x^6 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.84
\(\int \frac{x^4 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.85
\(\int \frac{x^2 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.86
\(\int \frac{4+x^2+3 x^4+5 x^6}{\left (2+3 x^2+x^4\right )^2} \, dx\)
3.87
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^2 \left (2+3 x^2+x^4\right )^2} \, dx\)
3.88
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^4 \left (2+3 x^2+x^4\right )^2} \, dx\)
3.89
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^6 \left (2+3 x^2+x^4\right )^2} \, dx\)
3.90
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^8 \left (2+3 x^2+x^4\right )^2} \, dx\)
3.91
\(\int \frac{x^{10} \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^3} \, dx\)
3.92
\(\int \frac{x^8 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^3} \, dx\)
3.93
\(\int \frac{x^6 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^3} \, dx\)
3.94
\(\int \frac{x^4 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^3} \, dx\)
3.95
\(\int \frac{x^2 \left (4+x^2+3 x^4+5 x^6\right )}{\left (2+3 x^2+x^4\right )^3} \, dx\)
3.96
\(\int \frac{4+x^2+3 x^4+5 x^6}{\left (2+3 x^2+x^4\right )^3} \, dx\)
3.97
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^2 \left (2+3 x^2+x^4\right )^3} \, dx\)
3.98
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^4 \left (2+3 x^2+x^4\right )^3} \, dx\)
3.99
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^6 \left (2+3 x^2+x^4\right )^3} \, dx\)
3.100
\(\int \frac{x^9 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.101
\(\int \frac{x^7 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.102
\(\int \frac{x^5 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.103
\(\int \frac{x^3 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.104
\(\int \frac{x \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.105
\(\int \frac{4+x^2+3 x^4+5 x^6}{x \left (3+2 x^2+x^4\right )^2} \, dx\)
3.106
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^3 \left (3+2 x^2+x^4\right )^2} \, dx\)
3.107
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^5 \left (3+2 x^2+x^4\right )^2} \, dx\)
3.108
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^7 \left (3+2 x^2+x^4\right )^2} \, dx\)
3.109
\(\int \frac{x^8 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.110
\(\int \frac{x^6 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.111
\(\int \frac{x^4 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.112
\(\int \frac{x^2 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.113
\(\int \frac{4+x^2+3 x^4+5 x^6}{\left (3+2 x^2+x^4\right )^2} \, dx\)
3.114
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^2 \left (3+2 x^2+x^4\right )^2} \, dx\)
3.115
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^4 \left (3+2 x^2+x^4\right )^2} \, dx\)
3.116
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^6 \left (3+2 x^2+x^4\right )^2} \, dx\)
3.117
\(\int \frac{x^{10} \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^3} \, dx\)
3.118
\(\int \frac{x^8 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^3} \, dx\)
3.119
\(\int \frac{x^6 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^3} \, dx\)
3.120
\(\int \frac{x^4 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^3} \, dx\)
3.121
\(\int \frac{x^2 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^3} \, dx\)
3.122
\(\int \frac{4+x^2+3 x^4+5 x^6}{\left (3+2 x^2+x^4\right )^3} \, dx\)
3.123
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^2 \left (3+2 x^2+x^4\right )^3} \, dx\)
3.124
\(\int \frac{4+x^2+3 x^4+5 x^6}{x^4 \left (3+2 x^2+x^4\right )^3} \, dx\)
3.125
\(\int \frac{x \left (d+e x^2+f x^4+g x^6\right )}{a+b x^2+c x^4} \, dx\)
3.126
\(\int \frac{x^4 \left (d+e x^2+f x^4+g x^6\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.127
\(\int \frac{x^2 \left (d+e x^2+f x^4+g x^6\right )}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.128
\(\int \frac{d+e x^2+f x^4+g x^6}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.129
\(\int \frac{d+e x^2+f x^4+g x^6}{x^2 \left (a+b x^2+c x^4\right )^2} \, dx\)
3.130
\(\int \frac{d+e x^2+f x^4+g x^6}{x^4 \left (a+b x^2+c x^4\right )^2} \, dx\)
3.131
\(\int x^2 \left (a+b x^2+c x^4\right )^p \left (3 a+b (5+2 p) x^2+c (7+4 p) x^4\right ) \, dx\)
3.132
\(\int \frac{x^5 \left (a+b x^2+c x^4\right )}{\sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.133
\(\int \frac{x^3 \left (a+b x^2+c x^4\right )}{\sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.134
\(\int \frac{x \left (a+b x^2+c x^4\right )}{\sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.135
\(\int \frac{a+b x^2+c x^4}{x \sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.136
\(\int \frac{a+b x^2+c x^4}{x^3 \sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.137
\(\int \frac{a+b x^2+c x^4}{x^5 \sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.138
\(\int \frac{a+b x^2+c x^4}{x^7 \sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.139
\(\int \frac{x^2 \left (a+b x^2+c x^4\right )}{\sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.140
\(\int \frac{a+b x^2+c x^4}{\sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.141
\(\int \frac{a+b x^2+c x^4}{x^2 \sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.142
\(\int \frac{a+b x^2+c x^4}{x^4 \sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.143
\(\int \frac{a+b x^2+c x^4}{x^6 \sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.144
\(\int \frac{a+b x^2+c x^4}{x^8 \sqrt{d-e x} \sqrt{d+e x}} \, dx\)
3.145
\(\int \frac{a+b x^2+c x^4}{x^{10} \sqrt{d-e x} \sqrt{d+e x}} \, dx\)
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