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Chapter 3
Listing of integrals
3.1
\(\int (b x+c x^2)^{7/2} \, dx\)
3.2
\(\int (3 i x+4 x^2)^{7/2} \, dx\)
3.3
\(\int (3 i x+4 x^2)^{5/2} \, dx\)
3.4
\(\int (3 i x+4 x^2)^{3/2} \, dx\)
3.5
\(\int \sqrt {3 i x+4 x^2} \, dx\)
3.6
\(\int (3 x-4 x^2)^{7/2} \, dx\)
3.7
\(\int (3 x-4 x^2)^{5/2} \, dx\)
3.8
\(\int (3 x-4 x^2)^{3/2} \, dx\)
3.9
\(\int \sqrt {3 x-4 x^2} \, dx\)
3.10
\(\int \sqrt {6 x-x^2} \, dx\)
3.11
\(\int \sqrt {5 x-9 x^2} \, dx\)
3.12
\(\int (x-x^2)^{3/2} \, dx\)
3.13
\(\int \sqrt {4 x+x^2} \, dx\)
3.14
\(\int \sqrt {-8 x+x^2} \, dx\)
3.15
\(\int \sqrt {-x+x^2} \, dx\)
3.16
\(\int \frac {1}{(b x+c x^2)^{7/2}} \, dx\)
3.17
\(\int \frac {1}{\sqrt {3 i x+4 x^2}} \, dx\)
3.18
\(\int \frac {1}{(3 i x+4 x^2)^{3/2}} \, dx\)
3.19
\(\int \frac {1}{(3 i x+4 x^2)^{5/2}} \, dx\)
3.20
\(\int \frac {1}{(3 i x+4 x^2)^{7/2}} \, dx\)
3.21
\(\int \frac {1}{\sqrt {3 x-4 x^2}} \, dx\)
3.22
\(\int \frac {1}{(3 x-4 x^2)^{3/2}} \, dx\)
3.23
\(\int \frac {1}{(3 x-4 x^2)^{5/2}} \, dx\)
3.24
\(\int \frac {1}{(3 x-4 x^2)^{7/2}} \, dx\)
3.25
\(\int \frac {1}{\sqrt {b x-b^2 x^2}} \, dx\)
3.26
\(\int \frac {1}{\sqrt {b x+b^2 x^2}} \, dx\)
3.27
\(\int \frac {1}{\sqrt {6 x-x^2}} \, dx\)
3.28
\(\int \frac {1}{\sqrt {4 x+x^2}} \, dx\)
3.29
\(\int \frac {1}{\sqrt {-2 x+x^2}} \, dx\)
3.30
\(\int (b x+c x^2)^{4/3} \, dx\)
3.31
\(\int \sqrt [3]{b x+c x^2} \, dx\)
3.32
\(\int \frac {1}{(b x+c x^2)^{2/3}} \, dx\)
3.33
\(\int \frac {1}{(b x+c x^2)^{5/3}} \, dx\)
3.34
\(\int \frac {1}{(b x+c x^2)^{8/3}} \, dx\)
3.35
\(\int (b x+c x^2)^{5/3} \, dx\)
3.36
\(\int (b x+c x^2)^{2/3} \, dx\)
3.37
\(\int \frac {1}{\sqrt [3]{b x+c x^2}} \, dx\)
3.38
\(\int \frac {1}{(b x+c x^2)^{4/3}} \, dx\)
3.39
\(\int \frac {1}{(b x+c x^2)^{7/3}} \, dx\)
3.40
\(\int (b x+c x^2)^{5/4} \, dx\)
3.41
\(\int (b x+c x^2)^{3/4} \, dx\)
3.42
\(\int \sqrt [4]{b x+c x^2} \, dx\)
3.43
\(\int \frac {1}{\sqrt [4]{b x+c x^2}} \, dx\)
3.44
\(\int \frac {1}{(b x+c x^2)^{3/4}} \, dx\)
3.45
\(\int \frac {1}{(b x+c x^2)^{5/4}} \, dx\)
3.46
\(\int \frac {1}{(b x+c x^2)^{9/4}} \, dx\)
3.47
\(\int \frac {1}{(b x+c x^2)^{13/4}} \, dx\)
3.48
\(\int (b x+c x^2)^p \, dx\)
3.49
\(\int (a+c x^2)^4 \, dx\)
3.50
\(\int (a+c x^2)^3 \, dx\)
3.51
\(\int (a+c x^2)^2 \, dx\)
3.52
\(\int (a+c x^2) \, dx\)
3.53
\(\int \frac {1}{a+c x^2} \, dx\)
3.54
\(\int \frac {1}{(a+c x^2)^2} \, dx\)
3.55
\(\int \frac {1}{(a+c x^2)^3} \, dx\)
3.56
\(\int (a+c x^2)^{5/2} \, dx\)
3.57
\(\int (a+c x^2)^{3/2} \, dx\)
3.58
\(\int \sqrt {a+c x^2} \, dx\)
3.59
\(\int \frac {1}{\sqrt {a+c x^2}} \, dx\)
3.60
\(\int \frac {1}{(a+c x^2)^{3/2}} \, dx\)
3.61
\(\int \frac {1}{(a+c x^2)^{5/2}} \, dx\)
3.62
\(\int \frac {1}{(a+c x^2)^{7/2}} \, dx\)
3.63
\(\int \frac {1}{(a+c x^2)^{9/2}} \, dx\)
3.64
\(\int (4+12 x+9 x^2)^{3/2} \, dx\)
3.65
\(\int \sqrt {4+12 x+9 x^2} \, dx\)
3.66
\(\int \frac {1}{\sqrt {4+12 x+9 x^2}} \, dx\)
3.67
\(\int \frac {1}{(4+12 x+9 x^2)^{3/2}} \, dx\)
3.68
\(\int \sqrt {4-12 x+9 x^2} \, dx\)
3.69
\(\int \frac {1}{\sqrt {4-12 x+9 x^2}} \, dx\)
3.70
\(\int \sqrt {-4+12 x-9 x^2} \, dx\)
3.71
\(\int \frac {1}{\sqrt {-4+12 x-9 x^2}} \, dx\)
3.72
\(\int \sqrt {-4-12 x-9 x^2} \, dx\)
3.73
\(\int \frac {1}{\sqrt {-4-12 x-9 x^2}} \, dx\)
3.74
\(\int (\frac {-1+b^2}{4 c}+b x+c x^2)^5 \, dx\)
3.75
\(\int (\frac {-4+b^2}{4 c}+b x+c x^2)^5 \, dx\)
3.76
\(\int (\frac {-9+b^2}{4 c}+b x+c x^2)^5 \, dx\)
3.77
\(\int (\frac {-16+b^2}{4 c}+b x+c x^2)^5 \, dx\)
3.78
\(\int \frac {1}{2+4 x+3 x^2} \, dx\)
3.79
\(\int \frac {1}{4-2 \sqrt {3} x+x^2} \, dx\)
3.80
\(\int \frac {1}{2+4 x-3 x^2} \, dx\)
3.81
\(\int \frac {1}{2+5 x+3 x^2} \, dx\)
3.82
\(\int \frac {1}{2+5 x-3 x^2} \, dx\)
3.83
\(\int \frac {1}{3+4 x+x^2} \, dx\)
3.84
\(\int \frac {1}{1+\pi x+2 x^2} \, dx\)
3.85
\(\int \frac {1}{1+\pi x-2 x^2} \, dx\)
3.86
\(\int \frac {1}{1+\pi x+3 x^2} \, dx\)
3.87
\(\int \frac {1}{1+\pi x-3 x^2} \, dx\)
3.88
\(\int \frac {1}{a+c x+b x^2} \, dx\)
3.89
\(\int \frac {1}{b+2 a x+b x^2} \, dx\)
3.90
\(\int \frac {1}{b+2 a x-b x^2} \, dx\)
3.91
\(\int \frac {1}{(2+4 x+3 x^2)^2} \, dx\)
3.92
\(\int \frac {1}{(2+4 x-3 x^2)^2} \, dx\)
3.93
\(\int \frac {1}{(2+5 x+3 x^2)^2} \, dx\)
3.94
\(\int \frac {1}{(2+5 x-3 x^2)^2} \, dx\)
3.95
\(\int \frac {1}{(a+c x+b x^2)^2} \, dx\)
3.96
\(\int \frac {1}{(b+2 a x+b x^2)^2} \, dx\)
3.97
\(\int \frac {1}{(b+2 a x-b x^2)^2} \, dx\)
3.98
\(\int \frac {1}{(\frac {a}{b})^{2/n}+x^2-2 (\frac {a}{b})^{\frac {1}{n}} x \cos (\frac {\pi -2 k \pi }{n})} \, dx\)
3.99
\(\int \frac {1}{a b+\sqrt {b^2-4 a b^3} x-b^2 x^2} \, dx\)
3.100
\(\int \frac {1}{a b-\sqrt {b^2-4 a b^3} x-b^2 x^2} \, dx\)
3.101
\(\int \frac {1}{1+x^2+2 x \cos (\frac {1}{7})} \, dx\)
3.102
\(\int \frac {1}{1+x^2+2 x \cos (\frac {\pi }{7})} \, dx\)
3.103
\(\int \sqrt {5-6 x+9 x^2} \, dx\)
3.104
\(\int \sqrt {3-4 x-4 x^2} \, dx\)
3.105
\(\int \sqrt {-8+6 x+9 x^2} \, dx\)
3.106
\(\int \sqrt {2+4 x+3 x^2} \, dx\)
3.107
\(\int \sqrt {2+4 x-3 x^2} \, dx\)
3.108
\(\int \sqrt {2+5 x+3 x^2} \, dx\)
3.109
\(\int \sqrt {2+5 x-3 x^2} \, dx\)
3.110
\(\int \sqrt {-2+4 x+3 x^2} \, dx\)
3.111
\(\int \sqrt {-2+4 x-3 x^2} \, dx\)
3.112
\(\int \sqrt {-2+5 x+3 x^2} \, dx\)
3.113
\(\int \sqrt {-2+5 x-3 x^2} \, dx\)
3.114
\(\int \frac {1}{\sqrt {5-6 x+9 x^2}} \, dx\)
3.115
\(\int \frac {1}{\sqrt {3-4 x-4 x^2}} \, dx\)
3.116
\(\int \frac {1}{\sqrt {-8+6 x+9 x^2}} \, dx\)
3.117
\(\int \frac {1}{\sqrt {2+4 x+3 x^2}} \, dx\)
3.118
\(\int \frac {1}{\sqrt {2+4 x-3 x^2}} \, dx\)
3.119
\(\int \frac {1}{\sqrt {2+5 x+3 x^2}} \, dx\)
3.120
\(\int \frac {1}{\sqrt {2+5 x-3 x^2}} \, dx\)
3.121
\(\int \frac {1}{\sqrt {-2+4 x+3 x^2}} \, dx\)
3.122
\(\int \frac {1}{\sqrt {-2+4 x-3 x^2}} \, dx\)
3.123
\(\int \frac {1}{\sqrt {-2+5 x+3 x^2}} \, dx\)
3.124
\(\int \frac {1}{\sqrt {-2+5 x-3 x^2}} \, dx\)
3.125
\(\int \frac {1}{\sqrt {\frac {b^2+4 c}{4 c}+b x+c x^2}} \, dx\)
3.126
\(\int \frac {1}{\sqrt {\frac {-b^2+4 c}{4 c}+b x-c x^2}} \, dx\)
3.127
\(\int \frac {1}{\sqrt {\frac {-b^2+c}{4 c}+b x-c x^2}} \, dx\)
3.128
\(\int \frac {1}{(2+3 x+x^2)^{3/2}} \, dx\)
3.129
\(\int \frac {1}{(27-24 x+4 x^2)^{3/2}} \, dx\)
3.130
\(\int \frac {x}{(5-4 x-x^2)^{3/2}} \, dx\)
3.131
\(\int \frac {1}{(5-4 x-x^2)^{5/2}} \, dx\)
3.132
\(\int (a+b x+c x^2)^p \, dx\)
3.133
\(\int (3+4 x+5 x^2)^p \, dx\)
3.134
\(\int (3+4 x+4 x^2)^p \, dx\)
3.135
\(\int (3+4 x+3 x^2)^p \, dx\)
3.136
\(\int (3+4 x+2 x^2)^p \, dx\)
3.137
\(\int (3+4 x+x^2)^p \, dx\)
3.138
\(\int (3+4 x)^p \, dx\)
3.139
\(\int (3+4 x-x^2)^p \, dx\)
3.140
\(\int (3+4 x-2 x^2)^p \, dx\)
3.141
\(\int (3+4 x-3 x^2)^p \, dx\)
3.142
\(\int (3+4 x-4 x^2)^p \, dx\)
3.143
\(\int (3+4 x-5 x^2)^p \, dx\)
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