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Chapter 3
Listing of integrals
3.1
\(\int x^2 (a x^2+b x^3+c x^4) \, dx\)
3.2
\(\int x (a x^2+b x^3+c x^4) \, dx\)
3.3
\(\int (a x^2+b x^3+c x^4) \, dx\)
3.4
\(\int \frac{a x^2+b x^3+c x^4}{x} \, dx\)
3.5
\(\int \frac{a x^2+b x^3+c x^4}{x^2} \, dx\)
3.6
\(\int x^2 (a x^2+b x^3+c x^4)^2 \, dx\)
3.7
\(\int x (a x^2+b x^3+c x^4)^2 \, dx\)
3.8
\(\int (a x^2+b x^3+c x^4)^2 \, dx\)
3.9
\(\int \frac{(a x^2+b x^3+c x^4)^2}{x} \, dx\)
3.10
\(\int \frac{(a x^2+b x^3+c x^4)^2}{x^2} \, dx\)
3.11
\(\int \frac{x^5}{a x^2+b x^3+c x^4} \, dx\)
3.12
\(\int \frac{x^4}{a x^2+b x^3+c x^4} \, dx\)
3.13
\(\int \frac{x^3}{a x^2+b x^3+c x^4} \, dx\)
3.14
\(\int \frac{x^2}{a x^2+b x^3+c x^4} \, dx\)
3.15
\(\int \frac{x}{a x^2+b x^3+c x^4} \, dx\)
3.16
\(\int \frac{1}{a x^2+b x^3+c x^4} \, dx\)
3.17
\(\int \frac{1}{x (a x^2+b x^3+c x^4)} \, dx\)
3.18
\(\int \frac{1}{x^2 (a x^2+b x^3+c x^4)} \, dx\)
3.19
\(\int \frac{x^8}{(a x^2+b x^3+c x^4)^2} \, dx\)
3.20
\(\int \frac{x^7}{(a x^2+b x^3+c x^4)^2} \, dx\)
3.21
\(\int \frac{x^6}{(a x^2+b x^3+c x^4)^2} \, dx\)
3.22
\(\int \frac{x^5}{(a x^2+b x^3+c x^4)^2} \, dx\)
3.23
\(\int \frac{x^4}{(a x^2+b x^3+c x^4)^2} \, dx\)
3.24
\(\int \frac{x^3}{(a x^2+b x^3+c x^4)^2} \, dx\)
3.25
\(\int \frac{x^2}{(a x^2+b x^3+c x^4)^2} \, dx\)
3.26
\(\int \frac{x}{(a x^2+b x^3+c x^4)^2} \, dx\)
3.27
\(\int \frac{1}{(a x^2+b x^3+c x^4)^2} \, dx\)
3.28
\(\int \frac{1}{x (a x^2+b x^3+c x^4)^2} \, dx\)
3.29
\(\int x^2 \sqrt{a x^2+b x^3+c x^4} \, dx\)
3.30
\(\int x \sqrt{a x^2+b x^3+c x^4} \, dx\)
3.31
\(\int \sqrt{a x^2+b x^3+c x^4} \, dx\)
3.32
\(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x} \, dx\)
3.33
\(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^2} \, dx\)
3.34
\(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^3} \, dx\)
3.35
\(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^4} \, dx\)
3.36
\(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^5} \, dx\)
3.37
\(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^6} \, dx\)
3.38
\(\int x (a x^2+b x^3+c x^4)^{3/2} \, dx\)
3.39
\(\int (a x^2+b x^3+c x^4)^{3/2} \, dx\)
3.40
\(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x} \, dx\)
3.41
\(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^2} \, dx\)
3.42
\(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^3} \, dx\)
3.43
\(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^4} \, dx\)
3.44
\(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^5} \, dx\)
3.45
\(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^6} \, dx\)
3.46
\(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^7} \, dx\)
3.47
\(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^8} \, dx\)
3.48
\(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^9} \, dx\)
3.49
\(\int \frac{x^3}{\sqrt{a x^2+b x^3+c x^4}} \, dx\)
3.50
\(\int \frac{x^2}{\sqrt{a x^2+b x^3+c x^4}} \, dx\)
3.51
\(\int \frac{x}{\sqrt{a x^2+b x^3+c x^4}} \, dx\)
3.52
\(\int \frac{1}{\sqrt{a x^2+b x^3+c x^4}} \, dx\)
3.53
\(\int \frac{1}{x \sqrt{a x^2+b x^3+c x^4}} \, dx\)
3.54
\(\int \frac{1}{x^2 \sqrt{a x^2+b x^3+c x^4}} \, dx\)
3.55
\(\int \frac{x^7}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.56
\(\int \frac{x^6}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.57
\(\int \frac{x^5}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.58
\(\int \frac{x^4}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.59
\(\int \frac{x^3}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.60
\(\int \frac{x^2}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.61
\(\int \frac{x}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.62
\(\int \frac{1}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.63
\(\int \frac{1}{x (a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.64
\(\int \frac{1}{x^2 (a x^2+b x^3+c x^4)^{3/2}} \, dx\)
3.65
\(\int x^m (a x+b x^3+c x^5) \, dx\)
3.66
\(\int x^2 (a x+b x^3+c x^5) \, dx\)
3.67
\(\int x (a x+b x^3+c x^5) \, dx\)
3.68
\(\int (a x+b x^3+c x^5) \, dx\)
3.69
\(\int \frac{a x+b x^3+c x^5}{x} \, dx\)
3.70
\(\int \frac{a x+b x^3+c x^5}{x^2} \, dx\)
3.71
\(\int \frac{a x+b x^3+c x^5}{x^3} \, dx\)
3.72
\(\int x^m (a x+b x^3+c x^5)^2 \, dx\)
3.73
\(\int x^2 (a x+b x^3+c x^5)^2 \, dx\)
3.74
\(\int x (a x+b x^3+c x^5)^2 \, dx\)
3.75
\(\int (a x+b x^3+c x^5)^2 \, dx\)
3.76
\(\int \frac{(a x+b x^3+c x^5)^2}{x} \, dx\)
3.77
\(\int \frac{(a x+b x^3+c x^5)^2}{x^2} \, dx\)
3.78
\(\int \frac{x^8}{a x+b x^3+c x^5} \, dx\)
3.79
\(\int \frac{x^7}{a x+b x^3+c x^5} \, dx\)
3.80
\(\int \frac{x^6}{a x+b x^3+c x^5} \, dx\)
3.81
\(\int \frac{x^5}{a x+b x^3+c x^5} \, dx\)
3.82
\(\int \frac{x^4}{a x+b x^3+c x^5} \, dx\)
3.83
\(\int \frac{x^3}{a x+b x^3+c x^5} \, dx\)
3.84
\(\int \frac{x^2}{a x+b x^3+c x^5} \, dx\)
3.85
\(\int \frac{x}{a x+b x^3+c x^5} \, dx\)
3.86
\(\int \frac{1}{a x+b x^3+c x^5} \, dx\)
3.87
\(\int \frac{1}{x (a x+b x^3+c x^5)} \, dx\)
3.88
\(\int \frac{1}{x^2 (a x+b x^3+c x^5)} \, dx\)
3.89
\(\int \frac{x^{11}}{(a x+b x^3+c x^5)^2} \, dx\)
3.90
\(\int \frac{x^{10}}{(a x+b x^3+c x^5)^2} \, dx\)
3.91
\(\int \frac{x^9}{(a x+b x^3+c x^5)^2} \, dx\)
3.92
\(\int \frac{x^8}{(a x+b x^3+c x^5)^2} \, dx\)
3.93
\(\int \frac{x^7}{(a x+b x^3+c x^5)^2} \, dx\)
3.94
\(\int \frac{x^6}{(a x+b x^3+c x^5)^2} \, dx\)
3.95
\(\int \frac{x^5}{(a x+b x^3+c x^5)^2} \, dx\)
3.96
\(\int \frac{x^4}{(a x+b x^3+c x^5)^2} \, dx\)
3.97
\(\int \frac{x^3}{(a x+b x^3+c x^5)^2} \, dx\)
3.98
\(\int \frac{x^2}{(a x+b x^3+c x^5)^2} \, dx\)
3.99
\(\int \frac{x}{(a x+b x^3+c x^5)^2} \, dx\)
3.100
\(\int \frac{1}{(a x+b x^3+c x^5)^2} \, dx\)
3.101
\(\int \frac{1}{x (a x+b x^3+c x^5)^2} \, dx\)
3.102
\(\int \frac{1}{x^2 (a x+b x^3+c x^5)^2} \, dx\)
3.103
\(\int \frac{1}{x^3 (a x+b x^3+c x^5)^2} \, dx\)
3.104
\(\int \frac{x}{\sqrt{a x+b x^3+c x^5}} \, dx\)
3.105
\(\int x^{3/2} \sqrt{a x+b x^3+c x^5} \, dx\)
3.106
\(\int \sqrt{x} \sqrt{a x+b x^3+c x^5} \, dx\)
3.107
\(\int \frac{\sqrt{a x+b x^3+c x^5}}{\sqrt{x}} \, dx\)
3.108
\(\int \frac{\sqrt{a x+b x^3+c x^5}}{x^{3/2}} \, dx\)
3.109
\(\int x^{3/2} (a x+b x^3+c x^5)^{3/2} \, dx\)
3.110
\(\int \sqrt{x} (a x+b x^3+c x^5)^{3/2} \, dx\)
3.111
\(\int \frac{(a x+b x^3+c x^5)^{3/2}}{\sqrt{x}} \, dx\)
3.112
\(\int \frac{(a x+b x^3+c x^5)^{3/2}}{x^{3/2}} \, dx\)
3.113
\(\int \frac{x^{3/2}}{\sqrt{a x+b x^3+c x^5}} \, dx\)
3.114
\(\int \frac{\sqrt{x}}{\sqrt{a x+b x^3+c x^5}} \, dx\)
3.115
\(\int \frac{1}{\sqrt{x} \sqrt{a x+b x^3+c x^5}} \, dx\)
3.116
\(\int \frac{1}{x^{3/2} \sqrt{a x+b x^3+c x^5}} \, dx\)
3.117
\(\int \frac{x^{3/2}}{(a x+b x^3+c x^5)^{3/2}} \, dx\)
3.118
\(\int \frac{\sqrt{x}}{(a x+b x^3+c x^5)^{3/2}} \, dx\)
3.119
\(\int \frac{1}{\sqrt{x} (a x+b x^3+c x^5)^{3/2}} \, dx\)
3.120
\(\int \frac{1}{x^{3/2} (a x+b x^3+c x^5)^{3/2}} \, dx\)
3.121
\(\int \frac{x^{\frac{3}{2} (-1+n)}}{(a x^{-1+n}+b x^n+c x^{1+n})^{3/2}} \, dx\)
3.122
\(\int \frac{x (d+e x^2)}{\sqrt{a x+b x^3+c x^5}} \, dx\)
3.123
\(\int \frac{1}{\sqrt{3 x^2-3 x^4+x^6}} \, dx\)
3.124
\(\int \frac{1}{\sqrt{x^2 (3-3 x^2+x^4)}} \, dx\)
3.125
\(\int \frac{1}{\sqrt{1-(1-x^2)^3}} \, dx\)
3.126
\(\int \sqrt{3 x^2-3 x^4+x^6} \, dx\)
3.127
\(\int \sqrt{x^2 (3-3 x^2+x^4)} \, dx\)
3.128
\(\int \sqrt{1-(1-x^2)^3} \, dx\)
3.129
\(\int \frac{1}{x \sqrt{a+b x+c x^2}} \, dx\)
3.130
\(\int \frac{1}{\sqrt{x^2 (a+b x+c x^2)}} \, dx\)
3.131
\(\int \frac{1}{\sqrt{x} \sqrt{x (a+b x+c x^2)}} \, dx\)
3.132
\(\int \frac{\sqrt{x}}{\sqrt{x^3 (a+b x+c x^2)}} \, dx\)
3.133
\(\int \frac{1}{x \sqrt{a+b x^2+c x^4}} \, dx\)
3.134
\(\int \frac{1}{\sqrt{x^2 (a+b x^2+c x^4)}} \, dx\)
3.135
\(\int \frac{1}{\sqrt{x} \sqrt{x (a+b x^2+c x^4)}} \, dx\)
3.136
\(\int \frac{\sqrt{x}}{\sqrt{x^3 (a+b x^2+c x^4)}} \, dx\)
3.137
\(\int \frac{1}{x \sqrt{3-3 x^2+x^4}} \, dx\)
3.138
\(\int \frac{1}{\sqrt{x^2 (3-3 x^2+x^4)}} \, dx\)
3.139
\(\int \frac{1}{\sqrt{x} \sqrt{x (3-3 x+x^2)}} \, dx\)
3.140
\(\int \frac{x^{-1+\frac{q}{2}}}{\sqrt{b x^n+c x^{2 n-q}+a x^q}} \, dx\)
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