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Chapter 3
Listing of integrals
3.1
\(\int \frac {(A+B x) (a+b x+c x^2)}{d+f x^2} \, dx\)
3.2
\(\int \frac {(A+B x) (a+b x+c x^2)^2}{d+f x^2} \, dx\)
3.3
\(\int \frac {(A+B x) (a+b x+c x^2)^3}{d+f x^2} \, dx\)
3.4
\(\int \frac {A+B x}{(a+b x+c x^2) (d+f x^2)} \, dx\)
3.5
\(\int \frac {A+B x}{(a+b x+c x^2)^2 (d+f x^2)} \, dx\)
3.6
\(\int \frac {(A+B x) \sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
3.7
\(\int \frac {A+B x}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
3.8
\(\int \frac {A+B x}{(a+b x+c x^2)^{3/2} (d-f x^2)} \, dx\)
3.9
\(\int \frac {A+B x}{(a+b x+c x^2)^{5/2} (d-f x^2)} \, dx\)
3.10
\(\int \frac {1+2 x}{(-1+x^2) \sqrt {-1+x+x^2}} \, dx\)
3.11
\(\int \frac {1+2 x}{(1+x^2) \sqrt {-1+x+x^2}} \, dx\)
3.12
\(\int \frac {a-c+b x}{(1+x^2) \sqrt {a+b x+c x^2}} \, dx\)
3.13
\(\int \frac {(A+B x) (a+b x+c x^2)}{d+e x+f x^2} \, dx\)
3.14
\(\int \frac {(A+B x) (a+b x+c x^2)^2}{d+e x+f x^2} \, dx\)
3.15
\(\int \frac {A+B x}{(a+b x+c x^2) (d+e x+f x^2)} \, dx\)
3.16
\(\int \frac {A+B x}{(a+b x+c x^2)^2 (d+e x+f x^2)} \, dx\)
3.17
\(\int \frac {g+h x}{(a+b x+c x^2) (a d+b d x+c d x^2)^2} \, dx\)
3.18
\(\int \frac {g+h x}{(a+b x+c x^2)^2 (a d+b d x+c d x^2)} \, dx\)
3.19
\(\int \frac {(A+B x) \sqrt {a+b x+c x^2}}{d+e x+f x^2} \, dx\)
3.20
\(\int \frac {(A+B x) (a+b x+c x^2)^{3/2}}{d+e x+f x^2} \, dx\)
3.21
\(\int \frac {A+B x}{(a+b x+c x^2) \sqrt {d+e x+f x^2}} \, dx\)
3.22
\(\int \frac {A+B x}{(a+c x^2) \sqrt {d+e x+f x^2}} \, dx\)
3.23
\(\int \frac {A+B x}{(a+b x+c x^2) \sqrt {d+f x^2}} \, dx\)
3.24
\(\int \frac {A+B x}{(a+c x^2) \sqrt {d+f x^2}} \, dx\)
3.25
\(\int \frac {2+x}{(2+4 x-3 x^2) \sqrt {1+3 x-2 x^2}} \, dx\)
3.26
\(\int \frac {2+x}{(2+4 x-3 x^2) (1+3 x-2 x^2)^{3/2}} \, dx\)
3.27
\(\int \frac {2+x}{(2+4 x-3 x^2) (1+3 x-2 x^2)^{5/2}} \, dx\)
3.28
\(\int \frac {2+x}{(2+4 x-3 x^2) \sqrt {1+3 x+2 x^2}} \, dx\)
3.29
\(\int \frac {2+x}{(2+4 x-3 x^2) (1+3 x+2 x^2)^{3/2}} \, dx\)
3.30
\(\int \frac {2+x}{(2+4 x-3 x^2) (1+3 x+2 x^2)^{5/2}} \, dx\)
3.31
\(\int \frac {1+x}{(4+2 x+x^2) \sqrt {5+2 x+x^2}} \, dx\)
3.32
\(\int \frac {4+x}{(4+2 x+x^2) \sqrt {5+2 x+x^2}} \, dx\)
3.33
\(\int \frac {1+2 x}{(3+x+x^2) \sqrt {5+x+x^2}} \, dx\)
3.34
\(\int \frac {x}{(3+x+x^2) \sqrt {5+x+x^2}} \, dx\)
3.35
\(\int \frac {A+B x}{\sqrt {d+e x+f x^2} (a e+b e x+b f x^2)^2} \, dx\)
3.36
\(\int \frac {(g+h x) \sqrt {a+b x+c x^2}}{(a d+b d x+c d x^2)^2} \, dx\)
3.37
\(\int \frac {3+2 x}{\sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
3.38
\(\int \frac {3+4 x}{\sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
3.39
\(\int \frac {(g+h x) \sqrt {a+b x+c x^2}}{(a d+b d x+c d x^2)^{3/2}} \, dx\)
3.40
\(\int x^2 \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2} \, dx\)
3.41
\(\int x \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2} \, dx\)
3.42
\(\int \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2} \, dx\)
3.43
\(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2}}{x} \, dx\)
3.44
\(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2}}{x^2} \, dx\)
3.45
\(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2}}{x^3} \, dx\)
3.46
\(\int x^2 \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2} \, dx\)
3.47
\(\int x \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2} \, dx\)
3.48
\(\int \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2} \, dx\)
3.49
\(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2}}{x} \, dx\)
3.50
\(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2}}{x^2} \, dx\)
3.51
\(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2}}{x^3} \, dx\)
3.52
\(\int \frac {x^2 \sqrt {a+c x^2}}{d+e x+f x^2} \, dx\)
3.53
\(\int \frac {x \sqrt {a+c x^2}}{d+e x+f x^2} \, dx\)
3.54
\(\int \frac {\sqrt {a+c x^2}}{d+e x+f x^2} \, dx\)
3.55
\(\int \frac {\sqrt {a+c x^2}}{x (d+e x+f x^2)} \, dx\)
3.56
\(\int \frac {\sqrt {a+c x^2}}{x^2 (d+e x+f x^2)} \, dx\)
3.57
\(\int \frac {\sqrt {a+c x^2}}{x^3 (d+e x+f x^2)} \, dx\)
3.58
\(\int \frac {x^2 (a+c x^2)^{3/2}}{d+e x+f x^2} \, dx\)
3.59
\(\int \frac {x (a+c x^2)^{3/2}}{d+e x+f x^2} \, dx\)
3.60
\(\int \frac {(a+c x^2)^{3/2}}{d+e x+f x^2} \, dx\)
3.61
\(\int \frac {(a+c x^2)^{3/2}}{x (d+e x+f x^2)} \, dx\)
3.62
\(\int \frac {(a+c x^2)^{3/2}}{x^2 (d+e x+f x^2)} \, dx\)
3.63
\(\int \frac {(a+c x^2)^{3/2}}{x^3 (d+e x+f x^2)} \, dx\)
3.64
\(\int \frac {x^3}{\sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
3.65
\(\int \frac {x^2}{\sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
3.66
\(\int \frac {x}{\sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
3.67
\(\int \frac {1}{\sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
3.68
\(\int \frac {1}{x \sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
3.69
\(\int \frac {1}{x^2 \sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
3.70
\(\int \frac {1}{x^3 \sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
3.71
\(\int \frac {x^3}{(a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.72
\(\int \frac {x^2}{(a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.73
\(\int \frac {x}{(a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.74
\(\int \frac {1}{(a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.75
\(\int \frac {1}{x (a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.76
\(\int \frac {1}{x^2 (a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.77
\(\int \frac {x^3 \sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
3.78
\(\int \frac {x^2 \sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
3.79
\(\int \frac {x \sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
3.80
\(\int \frac {\sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
3.81
\(\int \frac {\sqrt {a+b x+c x^2}}{x (d-f x^2)} \, dx\)
3.82
\(\int \frac {\sqrt {a+b x+c x^2}}{x^2 (d-f x^2)} \, dx\)
3.83
\(\int \frac {\sqrt {a+b x+c x^2}}{x^3 (d-f x^2)} \, dx\)
3.84
\(\int \frac {x^3 (a+b x+c x^2)^{3/2}}{d-f x^2} \, dx\)
3.85
\(\int \frac {x^2 (a+b x+c x^2)^{3/2}}{d-f x^2} \, dx\)
3.86
\(\int \frac {x (a+b x+c x^2)^{3/2}}{d-f x^2} \, dx\)
3.87
\(\int \frac {(a+b x+c x^2)^{3/2}}{d-f x^2} \, dx\)
3.88
\(\int \frac {(a+b x+c x^2)^{3/2}}{x (d-f x^2)} \, dx\)
3.89
\(\int \frac {(a+b x+c x^2)^{3/2}}{x^2 (d-f x^2)} \, dx\)
3.90
\(\int \frac {(a+b x+c x^2)^{3/2}}{x^3 (d-f x^2)} \, dx\)
3.91
\(\int \frac {(a+b x+c x^2)^{3/2}}{1-x^2} \, dx\)
3.92
\(\int \frac {\sqrt {-1-x+x^2}}{1-x^2} \, dx\)
3.93
\(\int \frac {(x+x^2)^{3/2}}{1+x^2} \, dx\)
3.94
\(\int \frac {x^4}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
3.95
\(\int \frac {x^3}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
3.96
\(\int \frac {x^2}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
3.97
\(\int \frac {x}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
3.98
\(\int \frac {1}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
3.99
\(\int \frac {1}{x \sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
3.100
\(\int \frac {1}{x^2 \sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
3.101
\(\int \frac {1}{x^3 \sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
3.102
\(\int \frac {x^4}{(a+b x+c x^2)^{3/2} (d-f x^2)} \, dx\)
3.103
\(\int \frac {x^3}{(a+b x+c x^2)^{3/2} (d-f x^2)} \, dx\)
3.104
\(\int \frac {x^2}{(a+b x+c x^2)^{3/2} (d-f x^2)} \, dx\)
3.105
\(\int \frac {x}{(a+b x+c x^2)^{3/2} (d-f x^2)} \, dx\)
3.106
\(\int \frac {1}{(a+b x+c x^2)^{3/2} (d-f x^2)} \, dx\)
3.107
\(\int \frac {1}{x (a+b x+c x^2)^{3/2} (d-f x^2)} \, dx\)
3.108
\(\int \frac {1}{x^2 (a+b x+c x^2)^{3/2} (d-f x^2)} \, dx\)
3.109
\(\int \frac {x^2 \sqrt {a+b x+c x^2}}{d+e x+f x^2} \, dx\)
3.110
\(\int \frac {x \sqrt {a+b x+c x^2}}{d+e x+f x^2} \, dx\)
3.111
\(\int \frac {\sqrt {a+b x+c x^2}}{d+e x+f x^2} \, dx\)
3.112
\(\int \frac {\sqrt {a+b x+c x^2}}{x (d+e x+f x^2)} \, dx\)
3.113
\(\int \frac {\sqrt {a+b x+c x^2}}{x^2 (d+e x+f x^2)} \, dx\)
3.114
\(\int \frac {x^3}{\sqrt {a+b x+c x^2} (d+e x+f x^2)} \, dx\)
3.115
\(\int \frac {x^2}{\sqrt {a+b x+c x^2} (d+e x+f x^2)} \, dx\)
3.116
\(\int \frac {x}{\sqrt {a+b x+c x^2} (d+e x+f x^2)} \, dx\)
3.117
\(\int \frac {1}{\sqrt {a+b x+c x^2} (d+e x+f x^2)} \, dx\)
3.118
\(\int \frac {1}{x \sqrt {a+b x+c x^2} (d+e x+f x^2)} \, dx\)
3.119
\(\int \frac {1}{x^2 \sqrt {a+b x+c x^2} (d+e x+f x^2)} \, dx\)
3.120
\(\int \frac {1}{x^3 \sqrt {a+b x+c x^2} (d+e x+f x^2)} \, dx\)
3.121
\(\int \frac {x^3}{(a+b x+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.122
\(\int \frac {x^2}{(a+b x+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.123
\(\int \frac {x}{(a+b x+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.124
\(\int \frac {1}{(a+b x+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.125
\(\int \frac {1}{x (a+b x+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
3.126
\(\int \frac {x^4}{\sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
3.127
\(\int \frac {x^3}{\sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
3.128
\(\int \frac {x^2}{\sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
3.129
\(\int \frac {x}{\sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
3.130
\(\int \frac {1}{\sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
3.131
\(\int \frac {1}{x \sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
3.132
\(\int \frac {1}{x^2 \sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
3.133
\(\int (2+3 x)^2 (30+31 x-12 x^2)^2 \sqrt {6+17 x+12 x^2} \, dx\)
3.134
\(\int (2+3 x) (30+31 x-12 x^2) \sqrt {6+17 x+12 x^2} \, dx\)
3.135
\(\int \frac {\sqrt {6+17 x+12 x^2}}{(2+3 x) (30+31 x-12 x^2)} \, dx\)
3.136
\(\int \frac {\sqrt {6+17 x+12 x^2}}{(2+3 x)^2 (30+31 x-12 x^2)^2} \, dx\)
3.137
\(\int \frac {\sqrt {6+17 x+12 x^2}}{(2+3 x)^3 (30+31 x-12 x^2)^3} \, dx\)
3.138
\(\int (-3+2 x) (-3 x+x^2)^{2/3} \, dx\)
3.139
\(\int ((-3+x) x)^{2/3} (-3+2 x) \, dx\)
3.140
\(\int \frac {x (9-9 x+2 x^2)}{\sqrt [3]{-3 x+x^2}} \, dx\)
3.141
\(\int \frac {x (9-9 x+2 x^2)}{\sqrt [3]{(-3+x) x}} \, dx\)
3.142
\(\int \frac {g+h x}{\sqrt [3]{-\frac {c g^2}{h^2}+9 c x^2} (g^2+3 h^2 x^2)} \, dx\)
3.143
\(\int \frac {g+h x}{\sqrt [3]{\frac {-c^2 g^2+b c g h+2 b^2 h^2}{9 c h^2}+b x+c x^2} (\frac {f (b^2-\frac {-c^2 g^2+b c g h+2 b^2 h^2}{3 h^2})}{c^2}+\frac {b f x}{c}+f x^2)} \, dx\)
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