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3
Listing of integrals
3.1
\(\int \frac{1}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.2
\(\int \frac{1}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.3
\(\int \frac{1}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.4
\(\int \frac{1}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.5
\(\int \frac{1}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.6
\(\int \frac{1}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.7
\(\int \frac{1}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.8
\(\int \frac{1}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.9
\(\int \frac{1}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
3.10
\(\int \frac{1}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.11
\(\int \frac{1}{\left (1+\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.12
\(\int \frac{1}{\left (1+\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.13
\(\int \frac{1}{\left (1+\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.14
\(\int \frac{1}{(3+x) \sqrt{1+x^3}} \, dx\)
3.15
\(\int \frac{1}{(3+x) \sqrt{1-x^3}} \, dx\)
3.16
\(\int \frac{1}{(3+x) \sqrt{-1+x^3}} \, dx\)
3.17
\(\int \frac{1}{(3+x) \sqrt{-1-x^3}} \, dx\)
3.18
\(\int \frac{1}{(c+d x) \sqrt [3]{-c^3+d^3 x^3}} \, dx\)
3.19
\(\int \frac{1}{(c+d x) \sqrt [3]{2 c^3+d^3 x^3}} \, dx\)
3.20
\(\int \frac{2^{2/3}-2 x}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.21
\(\int \frac{2^{2/3}+2 x}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.22
\(\int \frac{2^{2/3}+2 x}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.23
\(\int \frac{2^{2/3}-2 x}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.24
\(\int \frac{2^{2/3} \sqrt [3]{a}-2 \sqrt [3]{b} x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.25
\(\int \frac{2^{2/3} \sqrt [3]{a}+2 \sqrt [3]{b} x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.26
\(\int \frac{2^{2/3} \sqrt [3]{a}+2 \sqrt [3]{b} x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.27
\(\int \frac{2^{2/3} \sqrt [3]{a}-2 \sqrt [3]{b} x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.28
\(\int \frac{c-2 d x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
3.29
\(\int \frac{2+3 x}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.30
\(\int \frac{2+3 x}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.31
\(\int \frac{2+3 x}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.32
\(\int \frac{2+3 x}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.33
\(\int \frac{e+f x}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.34
\(\int \frac{e+f x}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.35
\(\int \frac{e+f x}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.36
\(\int \frac{e+f x}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.37
\(\int \frac{e+f x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.38
\(\int \frac{e+f x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.39
\(\int \frac{e+f x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.40
\(\int \frac{e+f x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.41
\(\int \frac{e+f x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
3.42
\(\int \frac{x}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.43
\(\int \frac{x}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.44
\(\int \frac{x}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.45
\(\int \frac{x}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.46
\(\int \frac{x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.47
\(\int \frac{x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.48
\(\int \frac{x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.49
\(\int \frac{x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.50
\(\int \frac{x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
3.51
\(\int \frac{1+x}{(2-x) \sqrt{1+x^3}} \, dx\)
3.52
\(\int \frac{1-x}{(2+x) \sqrt{1-x^3}} \, dx\)
3.53
\(\int \frac{1-x}{(2+x) \sqrt{-1+x^3}} \, dx\)
3.54
\(\int \frac{1+x}{(2-x) \sqrt{-1-x^3}} \, dx\)
3.55
\(\int \frac{\sqrt [3]{a}+\sqrt [3]{b} x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.56
\(\int \frac{\sqrt [3]{a}-\sqrt [3]{b} x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.57
\(\int \frac{\sqrt [3]{a}-\sqrt [3]{b} x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.58
\(\int \frac{\sqrt [3]{a}+\sqrt [3]{b} x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.59
\(\int \frac{c-2 d x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx\)
3.60
\(\int \frac{e+f x}{(2-x) \sqrt{1+x^3}} \, dx\)
3.61
\(\int \frac{e+f x}{(2+x) \sqrt{1-x^3}} \, dx\)
3.62
\(\int \frac{e+f x}{(2+x) \sqrt{-1+x^3}} \, dx\)
3.63
\(\int \frac{e+f x}{(2-x) \sqrt{-1-x^3}} \, dx\)
3.64
\(\int \frac{e+f x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.65
\(\int \frac{e+f x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.66
\(\int \frac{e+f x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.67
\(\int \frac{e+f x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.68
\(\int \frac{e+f x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx\)
3.69
\(\int \frac{x}{(2-x) \sqrt{1+x^3}} \, dx\)
3.70
\(\int \frac{x}{(2+x) \sqrt{1-x^3}} \, dx\)
3.71
\(\int \frac{x}{(2+x) \sqrt{-1+x^3}} \, dx\)
3.72
\(\int \frac{x}{(2-x) \sqrt{-1-x^3}} \, dx\)
3.73
\(\int \frac{x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.74
\(\int \frac{x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.75
\(\int \frac{x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.76
\(\int \frac{x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.77
\(\int \frac{x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx\)
3.78
\(\int \frac{1+\sqrt{3}+x}{\left (1-\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.79
\(\int \frac{1+\sqrt{3}-x}{\left (1-\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.80
\(\int \frac{1+\sqrt{3}-x}{\left (1-\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.81
\(\int \frac{1+\sqrt{3}+x}{\left (1-\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.82
\(\int \frac{\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.83
\(\int \frac{\left (1+\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.84
\(\int \frac{\left (1+\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.85
\(\int \frac{\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.86
\(\int \frac{1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{\left (1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{a+b x^3}} \, dx\)
3.87
\(\int \frac{1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{\left (1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{a-b x^3}} \, dx\)
3.88
\(\int \frac{1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{\left (1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.89
\(\int \frac{1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{\left (1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.90
\(\int \frac{1-\sqrt{3}+x}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.91
\(\int \frac{1-\sqrt{3}-x}{\left (1+\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.92
\(\int \frac{1-\sqrt{3}-x}{\left (1+\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.93
\(\int \frac{1-\sqrt{3}+x}{\left (1+\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.94
\(\int \frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.95
\(\int \frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.96
\(\int \frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.97
\(\int \frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.98
\(\int \frac{1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{\left (1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{a+b x^3}} \, dx\)
3.99
\(\int \frac{1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{\left (1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{a-b x^3}} \, dx\)
3.100
\(\int \frac{1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{\left (1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.101
\(\int \frac{1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{\left (1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.102
\(\int \frac{1+x}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.103
\(\int \frac{1+x}{\left (1-\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.104
\(\int \frac{e+f x}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.105
\(\int \frac{e+f x}{\left (1+\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.106
\(\int \frac{e+f x}{\left (1+\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.107
\(\int \frac{e+f x}{\left (1+\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.108
\(\int \frac{e+f x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.109
\(\int \frac{e+f x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.110
\(\int \frac{e+f x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.111
\(\int \frac{e+f x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.112
\(\int \frac{x}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.113
\(\int \frac{x}{\left (1+\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
3.114
\(\int \frac{x}{\left (1+\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
3.115
\(\int \frac{x}{\left (1+\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
3.116
\(\int \frac{x}{\left (1-\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
3.117
\(\int \frac{x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
3.118
\(\int \frac{x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
3.119
\(\int \frac{x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
3.120
\(\int \frac{x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
3.121
\(\int \frac{1+\sqrt{3}+x}{(c+d x) \sqrt{1+x^3}} \, dx\)
3.122
\(\int \frac{1+\sqrt{3}-x}{(c+d x) \sqrt{1-x^3}} \, dx\)
3.123
\(\int \frac{1+\sqrt{3}-x}{(c+d x) \sqrt{-1+x^3}} \, dx\)
3.124
\(\int \frac{1+\sqrt{3}+x}{(c+d x) \sqrt{-1-x^3}} \, dx\)
3.125
\(\int \frac{1-\sqrt{3}+x}{(c+d x) \sqrt{1+x^3}} \, dx\)
3.126
\(\int \frac{1-\sqrt{3}-x}{(c+d x) \sqrt{1-x^3}} \, dx\)
3.127
\(\int \frac{1-\sqrt{3}-x}{(c+d x) \sqrt{-1+x^3}} \, dx\)
3.128
\(\int \frac{1-\sqrt{3}+x}{(c+d x) \sqrt{-1-x^3}} \, dx\)
3.129
\(\int \frac{1+\sqrt{3}+x}{x \sqrt{1+x^3}} \, dx\)
3.130
\(\int \frac{1+\sqrt{3}-x}{x \sqrt{1-x^3}} \, dx\)
3.131
\(\int \frac{1+\sqrt{3}-x}{x \sqrt{-1+x^3}} \, dx\)
3.132
\(\int \frac{1+\sqrt{3}+x}{x \sqrt{-1-x^3}} \, dx\)
3.133
\(\int \frac{1-\sqrt{3}+x}{x \sqrt{1+x^3}} \, dx\)
3.134
\(\int \frac{1-\sqrt{3}-x}{x \sqrt{1-x^3}} \, dx\)
3.135
\(\int \frac{1-\sqrt{3}-x}{x \sqrt{-1+x^3}} \, dx\)
3.136
\(\int \frac{1-\sqrt{3}+x}{x \sqrt{-1-x^3}} \, dx\)
3.137
\(\int \frac{x}{(3+x) \sqrt{1+x^3}} \, dx\)
3.138
\(\int \frac{x}{(3+x) \sqrt{1-x^3}} \, dx\)
3.139
\(\int \frac{x}{(3+x) \sqrt{-1+x^3}} \, dx\)
3.140
\(\int \frac{x}{(3+x) \sqrt{-1-x^3}} \, dx\)
3.141
\(\int \frac{e+f x}{(c+d x) \sqrt{1+x^3}} \, dx\)
3.142
\(\int \frac{e+f x}{(c+d x) \sqrt{1-x^3}} \, dx\)
3.143
\(\int \frac{e+f x}{(c+d x) \sqrt{-1+x^3}} \, dx\)
3.144
\(\int \frac{e+f x}{(c+d x) \sqrt{-1-x^3}} \, dx\)
3.145
\(\int \frac{e+f x}{x \sqrt{1+x^3}} \, dx\)
3.146
\(\int \frac{e+f x}{x \sqrt{1-x^3}} \, dx\)
3.147
\(\int \frac{e+f x}{x \sqrt{-1+x^3}} \, dx\)
3.148
\(\int \frac{e+f x}{x \sqrt{-1-x^3}} \, dx\)
3.149
\(\int \frac{c-d x}{(c+d x) \sqrt [3]{2 c^3+d^3 x^3}} \, dx\)
3.150
\(\int \frac{e+f x}{(c+d x) \sqrt [3]{-c^3+d^3 x^3}} \, dx\)
3.151
\(\int x^2 (a+b x)^n \left (c+d x^3\right ) \, dx\)
3.152
\(\int x (a+b x)^n \left (c+d x^3\right ) \, dx\)
3.153
\(\int (a+b x)^n \left (c+d x^3\right ) \, dx\)
3.154
\(\int \frac{(a+b x)^n \left (c+d x^3\right )}{x} \, dx\)
3.155
\(\int x^2 (a+b x)^n \left (c+d x^3\right )^2 \, dx\)
3.156
\(\int x (a+b x)^n \left (c+d x^3\right )^2 \, dx\)
3.157
\(\int (a+b x)^n \left (c+d x^3\right )^2 \, dx\)
3.158
\(\int \frac{(a+b x)^n \left (c+d x^3\right )^2}{x} \, dx\)
3.159
\(\int x^2 (a+b x)^n \left (c+d x^3\right )^3 \, dx\)
3.160
\(\int x (a+b x)^n \left (c+d x^3\right )^3 \, dx\)
3.161
\(\int (a+b x)^n \left (c+d x^3\right )^3 \, dx\)
3.162
\(\int \frac{(a+b x)^n \left (c+d x^3\right )^3}{x} \, dx\)
3.163
\(\int \frac{x^5 (e+f x)^n}{a+b x^3} \, dx\)
3.164
\(\int \frac{x^4 (e+f x)^n}{a+b x^3} \, dx\)
3.165
\(\int \frac{x^3 (e+f x)^n}{a+b x^3} \, dx\)
3.166
\(\int \frac{x^2 (e+f x)^n}{a+b x^3} \, dx\)
3.167
\(\int \frac{x (e+f x)^n}{a+b x^3} \, dx\)
3.168
\(\int \frac{(e+f x)^n}{a+b x^3} \, dx\)
3.169
\(\int \frac{(e+f x)^n}{x \left (a+b x^3\right )} \, dx\)
3.170
\(\int \frac{(e+f x)^n}{x^2 \left (a+b x^3\right )} \, dx\)
3.171
\(\int \frac{x^2 (c+d x)^{1+n}}{a+b x^3} \, dx\)
3.172
\(\int \frac{x^m (e+f x)^n}{a+b x^3} \, dx\)
3.173
\(\int \frac{\sqrt{c+d x^3}}{a+b x} \, dx\)
3.174
\(\int \frac{\left (d^3+e^3 x^3\right )^p}{d+e x} \, dx\)
3.175
\(\int \frac{2-2 x-x^2}{\left (2+x^2\right ) \sqrt{1+x^3}} \, dx\)
3.176
\(\int \frac{2+2 x-x^2}{\left (2+x^2\right ) \sqrt{1-x^3}} \, dx\)
3.177
\(\int \frac{2+2 x-x^2}{\left (2+x^2\right ) \sqrt{-1+x^3}} \, dx\)
3.178
\(\int \frac{2-2 x-x^2}{\left (2+x^2\right ) \sqrt{-1-x^3}} \, dx\)
3.179
\(\int \frac{2-2 x-x^2}{\left (2+d+d x+x^2\right ) \sqrt{1+x^3}} \, dx\)
3.180
\(\int \frac{2+2 x-x^2}{\left (2-d+d x+x^2\right ) \sqrt{1-x^3}} \, dx\)
3.181
\(\int \frac{2+2 x-x^2}{\left (2-d+d x+x^2\right ) \sqrt{-1+x^3}} \, dx\)
3.182
\(\int \frac{2-2 x-x^2}{\left (2+d+d x+x^2\right ) \sqrt{-1-x^3}} \, dx\)
3.183
\(\int (d+e x)^3 \sqrt{a+c x^4} \, dx\)
3.184
\(\int (d+e x)^2 \sqrt{a+c x^4} \, dx\)
3.185
\(\int (d+e x) \sqrt{a+c x^4} \, dx\)
3.186
\(\int \sqrt{a+c x^4} \, dx\)
3.187
\(\int \frac{\sqrt{a+c x^4}}{d+e x} \, dx\)
3.188
\(\int \frac{\sqrt{a+c x^4}}{(d+e x)^2} \, dx\)
3.189
\(\int \frac{(d+e x)^3}{\sqrt{a+c x^4}} \, dx\)
3.190
\(\int \frac{(d+e x)^2}{\sqrt{a+c x^4}} \, dx\)
3.191
\(\int \frac{d+e x}{\sqrt{a+c x^4}} \, dx\)
3.192
\(\int \frac{1}{\sqrt{a+c x^4}} \, dx\)
3.193
\(\int \frac{1}{(d+e x) \sqrt{a+c x^4}} \, dx\)
3.194
\(\int \frac{1}{(d+e x)^2 \sqrt{a+c x^4}} \, dx\)
3.195
\(\int \frac{1}{(d+e x)^3 \sqrt{a+c x^4}} \, dx\)
3.196
\(\int \frac{(d+e x)^3}{\left (a+c x^4\right )^{3/2}} \, dx\)
3.197
\(\int \frac{(d+e x)^2}{\left (a+c x^4\right )^{3/2}} \, dx\)
3.198
\(\int \frac{d+e x}{\left (a+c x^4\right )^{3/2}} \, dx\)
3.199
\(\int \frac{1}{\left (a+c x^4\right )^{3/2}} \, dx\)
3.200
\(\int \frac{1}{(d+e x) \left (a+c x^4\right )^{3/2}} \, dx\)
3.201
\(\int \frac{1}{(d+e x)^2 \left (a+c x^4\right )^{3/2}} \, dx\)
3.202
\(\int \frac{x^3 (c+d x)^n}{a+b x^4} \, dx\)
3.203
\(\int \frac{x^3 (c+d x)^{1+n}}{a+b x^4} \, dx\)
3.204
\(\int \frac{1}{\left (c+d x+e x^2\right ) \sqrt{a+b x^4}} \, dx\)
3.205
\(\int \frac{\sqrt{a x^{23}}}{\sqrt{1+x^5}} \, dx\)
3.206
\(\int \frac{\sqrt{a x^{13}}}{\sqrt{1+x^5}} \, dx\)
3.207
\(\int \frac{\sqrt{a x^3}}{\sqrt{1+x^5}} \, dx\)
3.208
\(\int \frac{\sqrt{\frac{a}{x^7}}}{\sqrt{1+x^5}} \, dx\)
3.209
\(\int \frac{\sqrt{\frac{a}{x^{17}}}}{\sqrt{1+x^5}} \, dx\)
3.210
\(\int \frac{\sqrt{a x^6}}{x \left (1-x^4\right )} \, dx\)
3.211
\(\int \frac{\sqrt{a x^6}}{x-x^5} \, dx\)
3.212
\(\int \frac{\left (a x^6\right )^{3/2}}{x \left (1-x^4\right )} \, dx\)
3.213
\(\int \left (\frac{1}{1-x^4}-\frac{\sqrt{a x^6}}{x \left (1-x^4\right )}\right ) \, dx\)
3.214
\(\int \left (\frac{1}{1-x^4}-\frac{\sqrt{a x^6}}{x-x^5}\right ) \, dx\)
3.215
\(\int \frac{\sqrt{a x^3}}{x-x^3} \, dx\)
3.216
\(\int \frac{\sqrt{a x^4}}{\sqrt{1+x^2}} \, dx\)
3.217
\(\int \frac{\sqrt{a x^3}}{\sqrt{1+x^2}} \, dx\)
3.218
\(\int \frac{\sqrt{a x^2}}{\sqrt{1+x^2}} \, dx\)
3.219
\(\int \frac{\sqrt{a x}}{\sqrt{1+x^2}} \, dx\)
3.220
\(\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{1+x^2}} \, dx\)
3.221
\(\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{1+x^2}} \, dx\)
3.222
\(\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{1+x^2}} \, dx\)
3.223
\(\int \frac{\sqrt{\frac{a}{x^4}}}{\sqrt{1+x^2}} \, dx\)
3.224
\(\int \frac{\sqrt{a x^4}}{\sqrt{1+x^3}} \, dx\)
3.225
\(\int \frac{\sqrt{a x^3}}{\sqrt{1+x^3}} \, dx\)
3.226
\(\int \frac{\sqrt{a x^2}}{\sqrt{1+x^3}} \, dx\)
3.227
\(\int \frac{\sqrt{a x}}{\sqrt{1+x^3}} \, dx\)
3.228
\(\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{1+x^3}} \, dx\)
3.229
\(\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{1+x^3}} \, dx\)
3.230
\(\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{1+x^3}} \, dx\)
3.231
\(\int \frac{\sqrt{\frac{a}{x^4}}}{\sqrt{1+x^3}} \, dx\)
3.232
\(\int \frac{\sqrt{a x^{2 n}}}{\sqrt{1+x^n}} \, dx\)
3.233
\(\int \frac{\sqrt{a x^n}}{\sqrt{1+x^n}} \, dx\)
3.234
\(\int \frac{\sqrt{a x^{n/2}}}{\sqrt{1+x^n}} \, dx\)
3.235
\(\int \left (\frac{\sqrt{a x^{2 n}}}{\sqrt{1+x^n}}+\frac{2 x^{-n} \sqrt{a x^{2 n}}}{(2+n) \sqrt{1+x^n}}\right ) \, dx\)
3.236
\(\int \frac{\sqrt{a x}}{\sqrt{d+e x} \sqrt{e+f x}} \, dx\)
3.237
\(\int \left (a x^m\right )^r \, dx\)
3.238
\(\int \left (a x^m\right )^r \left (b x^n\right )^s \, dx\)
3.239
\(\int \left (a x^m\right )^r \left (b x^n\right )^s \left (c x^p\right )^t \, dx\)
3.240
\(\int \frac{x^2}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx\)
3.241
\(\int \frac{x}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx\)
3.242
\(\int \frac{1}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx\)
3.243
\(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{c+b x}\right )} \, dx\)
3.244
\(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{c+b x}\right )} \, dx\)
3.245
\(\int \frac{x^2}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
3.246
\(\int \frac{x}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
3.247
\(\int \frac{1}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
3.248
\(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
3.249
\(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
3.250
\(\int \frac{x^2}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
3.251
\(\int \frac{x}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
3.252
\(\int \frac{1}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
3.253
\(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
3.254
\(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
3.255
\(\int \frac{1}{\sqrt{x}+\sqrt{1+x}} \, dx\)
3.256
\(\int \frac{1}{\sqrt{-1+x}+\sqrt{x}} \, dx\)
3.257
\(\int \frac{1}{\sqrt{-1+x}+\sqrt{1+x}} \, dx\)
3.258
\(\int x^3 \left (\sqrt{1-x}+\sqrt{1+x}\right )^2 \, dx\)
3.259
\(\int x^2 \left (\sqrt{1-x}+\sqrt{1+x}\right )^2 \, dx\)
3.260
\(\int x \left (\sqrt{1-x}+\sqrt{1+x}\right )^2 \, dx\)
3.261
\(\int \left (\sqrt{1-x}+\sqrt{1+x}\right )^2 \, dx\)
3.262
\(\int \frac{\left (\sqrt{1-x}+\sqrt{1+x}\right )^2}{x} \, dx\)
3.263
\(\int \frac{\left (\sqrt{1-x}+\sqrt{1+x}\right )^2}{x^2} \, dx\)
3.264
\(\int \frac{\left (\sqrt{1-x}+\sqrt{1+x}\right )^2}{x^3} \, dx\)
3.265
\(\int \frac{x^3}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
3.266
\(\int \frac{x^2}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
3.267
\(\int \frac{x}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
3.268
\(\int \frac{1}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
3.269
\(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{a+c x}\right )} \, dx\)
3.270
\(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{a+c x}\right )} \, dx\)
3.271
\(\int \frac{x^3}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
3.272
\(\int \frac{x^2}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
3.273
\(\int \frac{x}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
3.274
\(\int \frac{1}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
3.275
\(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
3.276
\(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
3.277
\(\int \frac{x^4}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
3.278
\(\int \frac{x^3}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
3.279
\(\int \frac{x^2}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
3.280
\(\int \frac{x}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
3.281
\(\int \frac{1}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
3.282
\(\int \sqrt{1-x} \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
3.283
\(\int x^3 \left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
3.284
\(\int x^2 \left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
3.285
\(\int x \left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
3.286
\(\int \left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
3.287
\(\int \frac{\left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right )}{x} \, dx\)
3.288
\(\int \frac{\left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right )}{x^2} \, dx\)
3.289
\(\int \frac{\left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right )}{x^3} \, dx\)
3.290
\(\int \frac{\sqrt{1-x}+\sqrt{1+x}}{-\sqrt{1-x}+\sqrt{1+x}} \, dx\)
3.291
\(\int \frac{-\sqrt{-1+x}+\sqrt{1+x}}{\sqrt{-1+x}+\sqrt{1+x}} \, dx\)
3.292
\(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
3.293
\(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^3 \, dx\)
3.294
\(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^2 \, dx\)
3.295
\(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right ) \, dx\)
3.296
\(\int \frac{1}{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}} \, dx\)
3.297
\(\int \frac{1}{\left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^2} \, dx\)
3.298
\(\int \frac{1}{\left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^3} \, dx\)
3.299
\(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^{5/2} \, dx\)
3.300
\(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^{3/2} \, dx\)
3.301
\(\int \sqrt{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}} \, dx\)
3.302
\(\int \frac{1}{\sqrt{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}}} \, dx\)
3.303
\(\int \frac{1}{\left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^{3/2}} \, dx\)
3.304
\(\int \frac{1}{\left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^{5/2}} \, dx\)
3.305
\(\int \sqrt{x-\sqrt{-4+x^2}} \, dx\)
3.306
\(\int \sqrt{a x+b \sqrt{c+\frac{a^2 x^2}{b^2}}} \, dx\)
3.307
\(\int \sqrt{1+\sqrt{1-x^2}} \, dx\)
3.308
\(\int \sqrt{1+\sqrt{1+x^2}} \, dx\)
3.309
\(\int \sqrt{5+\sqrt{25+x^2}} \, dx\)
3.310
\(\int \sqrt{a+b \sqrt{\frac{a^2}{b^2}+c x^2}} \, dx\)
3.311
\(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
3.312
\(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^3 \, dx\)
3.313
\(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^2 \, dx\)
3.314
\(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right ) \, dx\)
3.315
\(\int \frac{1}{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}} \, dx\)
3.316
\(\int \frac{1}{\left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^2} \, dx\)
3.317
\(\int \frac{1}{\left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^3} \, dx\)
3.318
\(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^{5/2} \, dx\)
3.319
\(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^{3/2} \, dx\)
3.320
\(\int \sqrt{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}} \, dx\)
3.321
\(\int \frac{1}{\sqrt{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}}} \, dx\)
3.322
\(\int \frac{1}{\left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^{3/2}} \, dx\)
3.323
\(\int \frac{1}{\left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^{5/2}} \, dx\)
3.324
\(\int \left (a+x^2\right )^2 \left (x+\sqrt{a+x^2}\right )^n \, dx\)
3.325
\(\int \left (a+x^2\right ) \left (x+\sqrt{a+x^2}\right )^n \, dx\)
3.326
\(\int \left (x+\sqrt{a+x^2}\right )^n \, dx\)
3.327
\(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{a+x^2} \, dx\)
3.328
\(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^2} \, dx\)
3.329
\(\int \left (a+x^2\right )^2 \left (x-\sqrt{a+x^2}\right )^n \, dx\)
3.330
\(\int \left (a+x^2\right ) \left (x-\sqrt{a+x^2}\right )^n \, dx\)
3.331
\(\int \left (x-\sqrt{a+x^2}\right )^n \, dx\)
3.332
\(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{a+x^2} \, dx\)
3.333
\(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^2} \, dx\)
3.334
\(\int \left (a+x^2\right )^{5/2} \left (x+\sqrt{a+x^2}\right )^n \, dx\)
3.335
\(\int \left (a+x^2\right )^{3/2} \left (x+\sqrt{a+x^2}\right )^n \, dx\)
3.336
\(\int \sqrt{a+x^2} \left (x+\sqrt{a+x^2}\right )^n \, dx\)
3.337
\(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{\sqrt{a+x^2}} \, dx\)
3.338
\(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^{3/2}} \, dx\)
3.339
\(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^{5/2}} \, dx\)
3.340
\(\int \left (a+x^2\right )^{5/2} \left (x-\sqrt{a+x^2}\right )^n \, dx\)
3.341
\(\int \left (a+x^2\right )^{3/2} \left (x-\sqrt{a+x^2}\right )^n \, dx\)
3.342
\(\int \sqrt{a+x^2} \left (x-\sqrt{a+x^2}\right )^n \, dx\)
3.343
\(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{\sqrt{a+x^2}} \, dx\)
3.344
\(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^{3/2}} \, dx\)
3.345
\(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^{5/2}} \, dx\)
3.346
\(\int \left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right )^2 \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
3.347
\(\int \left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right ) \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
3.348
\(\int \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
3.349
\(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \, dx\)
3.350
\(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right )^2} \, dx\)
3.351
\(\int \left (d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right )^n \, dx\)
3.352
\(\int \frac{\left (d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right )^n}{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \, dx\)
3.353
\(\int \left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right )^{3/2} \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
3.354
\(\int \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
3.355
\(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}} \, dx\)
3.356
\(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right )^{3/2}} \, dx\)
3.357
\(\int \frac{\left (d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right )^n}{\sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}} \, dx\)
3.358
\(\int \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
3.359
\(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}} \, dx\)
3.360
\(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\left (a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}\right )^{3/2}} \, dx\)
3.361
\(\int \frac{\left (d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right )^n}{\sqrt{\frac{a f^2 g+e g x (2 d+e x)}{f^2}}} \, dx\)
3.362
\(\int \frac{1}{(a+b x) \sqrt{c+d x^2} \sqrt{e+f x^2}} \, dx\)
3.363
\(\int \frac{e-2 f x^2}{e^2+4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\)
3.364
\(\int \frac{e-2 f x^2}{e^2-4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\)
3.365
\(\int \frac{e-4 f x^3}{e^2+4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\)
3.366
\(\int \frac{e-4 f x^3}{e^2-4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\)
3.367
\(\int \frac{e-2 f (-1+n) x^n}{e^2+4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
3.368
\(\int \frac{e-2 f (-1+n) x^n}{e^2-4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
3.369
\(\int \frac{x}{e^2+4 e f x^2+4 d f x^4+4 f^2 x^4} \, dx\)
3.370
\(\int \frac{x}{e^2+4 e f x^2-4 d f x^4+4 f^2 x^4} \, dx\)
3.371
\(\int \frac{x^2 \left (3 e+2 f x^2\right )}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^6} \, dx\)
3.372
\(\int \frac{x^2 \left (3 e+2 f x^2\right )}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^6} \, dx\)
3.373
\(\int \frac{x^m \left (e (1+m)+2 f (-1+m) x^2\right )}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^{2+2 m}} \, dx\)
3.374
\(\int \frac{x^m \left (e (1+m)+2 f (-1+m) x^2\right )}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^{2+2 m}} \, dx\)
3.375
\(\int \frac{x \left (2 e-2 f x^3\right )}{e^2+4 e f x^3+4 d f x^4+4 f^2 x^6} \, dx\)
3.376
\(\int \frac{x \left (2 e-2 f x^3\right )}{e^2+4 e f x^3-4 d f x^4+4 f^2 x^6} \, dx\)
3.377
\(\int \frac{x^2}{e^2+4 e f x^3+4 d f x^6+4 f^2 x^6} \, dx\)
3.378
\(\int \frac{x^2}{e^2+4 e f x^3-4 d f x^6+4 f^2 x^6} \, dx\)
3.379
\(\int \frac{x^m \left (e (1+m)+2 f (-2+m) x^3\right )}{e^2+4 e f x^3+4 f^2 x^6+4 d f x^{2+2 m}} \, dx\)
3.380
\(\int \frac{x^m \left (e (1+m)+2 f (-2+m) x^3\right )}{e^2+4 e f x^3+4 f^2 x^6-4 d f x^{2+2 m}} \, dx\)
3.381
\(\int \frac{x^m \left (e (1+m)+2 f (1+m-n) x^n\right )}{e^2+4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
3.382
\(\int \frac{x^m \left (e (1+m)+2 f (1+m-n) x^n\right )}{e^2-4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
3.383
\(\int \frac{x^5}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.384
\(\int \frac{x^3}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.385
\(\int \frac{x}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.386
\(\int \frac{1}{x \left (a c+b c x^2+d \sqrt{a+b x^2}\right )} \, dx\)
3.387
\(\int \frac{1}{x^3 \left (a c+b c x^2+d \sqrt{a+b x^2}\right )} \, dx\)
3.388
\(\int \frac{x^2}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.389
\(\int \frac{1}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.390
\(\int \frac{1}{x^2 \left (a c+b c x^2+d \sqrt{a+b x^2}\right )} \, dx\)
3.391
\(\int \frac{x^8}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.392
\(\int \frac{x^5}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.393
\(\int \frac{x^2}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.394
\(\int \frac{1}{x \left (a c+b c x^3+d \sqrt{a+b x^3}\right )} \, dx\)
3.395
\(\int \frac{1}{x^4 \left (a c+b c x^3+d \sqrt{a+b x^3}\right )} \, dx\)
3.396
\(\int \frac{x^3}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.397
\(\int \frac{x}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.398
\(\int \frac{1}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.399
\(\int \frac{1}{x^2 \left (a c+b c x^3+d \sqrt{a+b x^3}\right )} \, dx\)
3.400
\(\int \frac{1}{x^3 \left (a c+b c x^3+d \sqrt{a+b x^3}\right )} \, dx\)
3.401
\(\int \frac{1}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx\)
3.402
\(\int \frac{x^m}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx\)
3.403
\(\int \frac{x^{-1+n}}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx\)
3.404
\(\int \frac{1}{\sqrt{x}+4 x^{3/2}} \, dx\)
3.405
\(\int \frac{1}{\sqrt{x}-x^{5/2}} \, dx\)
3.406
\(\int \frac{1}{-\sqrt [4]{x}+\sqrt{x}} \, dx\)
3.407
\(\int \frac{1}{\sqrt [3]{x}+\sqrt{x}} \, dx\)
3.408
\(\int \frac{1}{\sqrt [4]{x}+\sqrt{x}} \, dx\)
3.409
\(\int \frac{1}{-\sqrt [3]{x}+x^{2/3}} \, dx\)
3.410
\(\int \frac{1}{\frac{1}{\sqrt [4]{x}}+\sqrt{x}} \, dx\)
3.411
\(\int \frac{1}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\)
3.412
\(\int \frac{1}{\frac{1}{\sqrt [3]{x}}+\frac{1}{\sqrt [4]{x}}} \, dx\)
3.413
\(\int \frac{1}{-\frac{1}{\sqrt [3]{x}}+\sqrt{x}} \, dx\)
3.414
\(\int \frac{\sqrt{x}}{x+x^2} \, dx\)
3.415
\(\int \frac{x}{4 \sqrt{x}+x} \, dx\)
3.416
\(\int \frac{\sqrt{x}}{\sqrt [3]{x}+x} \, dx\)
3.417
\(\int \frac{\sqrt [3]{x}}{\sqrt [4]{x}+\sqrt{x}} \, dx\)
3.418
\(\int \frac{\sqrt{x}}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\)
3.419
\(\int \frac{\sqrt{x}}{-\frac{1}{\sqrt [3]{x}}+\sqrt{x}} \, dx\)
3.420
\(\int \frac{\sqrt{b-\frac{a}{x}} x^m}{\sqrt{a-b x}} \, dx\)
3.421
\(\int \frac{\sqrt{b-\frac{a}{x}} x^2}{\sqrt{a-b x}} \, dx\)
3.422
\(\int \frac{\sqrt{b-\frac{a}{x}} x}{\sqrt{a-b x}} \, dx\)
3.423
\(\int \frac{\sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \, dx\)
3.424
\(\int \frac{\sqrt{b-\frac{a}{x}}}{x \sqrt{a-b x}} \, dx\)
3.425
\(\int \frac{\sqrt{b-\frac{a}{x}}}{x^2 \sqrt{a-b x}} \, dx\)
3.426
\(\int \left (a+\frac{b}{x}\right )^m (c+d x)^n \, dx\)
3.427
\(\int \left (a+\frac{b}{x}\right )^m (c+d x)^2 \, dx\)
3.428
\(\int \left (a+\frac{b}{x}\right )^m (c+d x) \, dx\)
3.429
\(\int \left (a+\frac{b}{x}\right )^m \, dx\)
3.430
\(\int \frac{\left (a+\frac{b}{x}\right )^m}{c+d x} \, dx\)
3.431
\(\int \frac{\left (a+\frac{b}{x}\right )^m}{(c+d x)^2} \, dx\)
3.432
\(\int \frac{\left (a+\frac{b}{x}\right )^m}{(c+d x)^3} \, dx\)
3.433
\(\int \frac{\left (a+\frac{b}{x}\right )^m}{(c+d x)^4} \, dx\)
3.434
\(\int \frac{\sqrt{b-\frac{a}{x^2}} x^m}{\sqrt{a-b x^2}} \, dx\)
3.435
\(\int \frac{\sqrt{b-\frac{a}{x^2}} x^2}{\sqrt{a-b x^2}} \, dx\)
3.436
\(\int \frac{\sqrt{b-\frac{a}{x^2}} x}{\sqrt{a-b x^2}} \, dx\)
3.437
\(\int \frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \, dx\)
3.438
\(\int \frac{\sqrt{b-\frac{a}{x^2}}}{x \sqrt{a-b x^2}} \, dx\)
3.439
\(\int \frac{\sqrt{b-\frac{a}{x^2}}}{x^2 \sqrt{a-b x^2}} \, dx\)
3.440
\(\int \frac{(c+d x)^{3/2}}{\sqrt{a+\frac{b}{x^2}}} \, dx\)
3.441
\(\int \frac{-1+x^3}{\left (-4 x+x^4\right )^{2/3}} \, dx\)
3.442
\(\int \left (2-x^2\right ) \sqrt [4]{6 x-x^3} \, dx\)
3.443
\(\int \left (1+x^4\right ) \sqrt{5 x+x^5} \, dx\)
3.444
\(\int \left (2+5 x^4\right ) \sqrt{2 x+x^5} \, dx\)
3.445
\(\int \frac{x+3 x^2}{\sqrt{x^2+2 x^3}} \, dx\)
3.446
\(\int \frac{2+\sqrt [3]{1-5 x}}{3+\sqrt [3]{1-5 x}} \, dx\)
3.447
\(\int \frac{1+\sqrt{x}}{-1+\sqrt{x}} \, dx\)
3.448
\(\int \frac{1-\sqrt{2+3 x}}{1+\sqrt{2+3 x}} \, dx\)
3.449
\(\int \frac{-1+\sqrt{a+b x}}{1+\sqrt{a+b x}} \, dx\)
3.450
\(\int \frac{a+b n x^{-1+n}}{a x+b x^n} \, dx\)
3.451
\(\int \frac{x^{-n} \left (a+b n x^{-1+n}\right )}{b+a x^{1-n}} \, dx\)
3.452
\(\int x \left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (2 a d+(3 b d+3 a e+b d m+a e n) x+(4 c d+4 b e+4 a f+2 c d m+b e m+b e n+2 a f n) x^2+(5 c e+5 b f+5 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(6 c f+6 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (7+2 m+3 n) x^5\right ) \, dx\)
3.453
\(\int \left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (a d+(2 b d+2 a e+b d m+a e n) x+(3 c d+3 b e+3 a f+2 c d m+b e m+b e n+2 a f n) x^2+(4 c e+4 b f+4 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(5 c f+5 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (6+2 m+3 n) x^5\right ) \, dx\)
3.454
\(\int \left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (b d+a e+b d m+a e n+(2 c d+2 b e+2 a f+2 c d m+b e m+b e n+2 a f n) x+(3 c e+3 b f+3 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^2+(4 c f+4 b g+2 c f m+b g m+2 c f n+3 b g n) x^3+c g (5+2 m+3 n) x^4\right ) \, dx\)
3.455
\(\int \frac{\left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (-a d+(b d m+a e n) x+(c d+b e+a f+2 c d m+b e m+b e n+2 a f n) x^2+(2 c e+2 b f+2 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(3 c f+3 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (4+2 m+3 n) x^5\right )}{x^2} \, dx\)
3.456
\(\int \frac{\left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (-2 a d+(-b d-a e+b d m+a e n) x+(2 c d m+b e m+b e n+2 a f n) x^2+(c e+b f+a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(2 c f+2 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (3+2 m+3 n) x^5\right )}{x^3} \, dx\)
3.457
\(\int x^3 \left (a+b \sqrt{c+d x}\right )^2 \, dx\)
3.458
\(\int x^2 \left (a+b \sqrt{c+d x}\right )^2 \, dx\)
3.459
\(\int x \left (a+b \sqrt{c+d x}\right )^2 \, dx\)
3.460
\(\int \left (a+b \sqrt{c+d x}\right )^2 \, dx\)
3.461
\(\int \frac{\left (a+b \sqrt{c+d x}\right )^2}{x} \, dx\)
3.462
\(\int \frac{\left (a+b \sqrt{c+d x}\right )^2}{x^2} \, dx\)
3.463
\(\int \frac{\left (a+b \sqrt{c+d x}\right )^2}{x^3} \, dx\)
3.464
\(\int x^3 \sqrt{a+b \sqrt{c+d x}} \, dx\)
3.465
\(\int x^2 \sqrt{a+b \sqrt{c+d x}} \, dx\)
3.466
\(\int x \sqrt{a+b \sqrt{c+d x}} \, dx\)
3.467
\(\int \sqrt{a+b \sqrt{c+d x}} \, dx\)
3.468
\(\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x} \, dx\)
3.469
\(\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x^2} \, dx\)
3.470
\(\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x^3} \, dx\)
3.471
\(\int \frac{x^3}{a+b \sqrt{c+d x}} \, dx\)
3.472
\(\int \frac{x^2}{a+b \sqrt{c+d x}} \, dx\)
3.473
\(\int \frac{x}{a+b \sqrt{c+d x}} \, dx\)
3.474
\(\int \frac{1}{a+b \sqrt{c+d x}} \, dx\)
3.475
\(\int \frac{1}{x \left (a+b \sqrt{c+d x}\right )} \, dx\)
3.476
\(\int \frac{1}{x^2 \left (a+b \sqrt{c+d x}\right )} \, dx\)
3.477
\(\int \frac{1}{x^3 \left (a+b \sqrt{c+d x}\right )} \, dx\)
3.478
\(\int \frac{x^3}{\left (a+b \sqrt{c+d x}\right )^2} \, dx\)
3.479
\(\int \frac{x^2}{\left (a+b \sqrt{c+d x}\right )^2} \, dx\)
3.480
\(\int \frac{x}{\left (a+b \sqrt{c+d x}\right )^2} \, dx\)
3.481
\(\int \frac{1}{\left (a+b \sqrt{c+d x}\right )^2} \, dx\)
3.482
\(\int \frac{1}{x \left (a+b \sqrt{c+d x}\right )^2} \, dx\)
3.483
\(\int \frac{1}{x^2 \left (a+b \sqrt{c+d x}\right )^2} \, dx\)
3.484
\(\int \frac{1}{x^3 \left (a+b \sqrt{c+d x}\right )^2} \, dx\)
3.485
\(\int \frac{x^3}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.486
\(\int \frac{x^2}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.487
\(\int \frac{x}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.488
\(\int \frac{1}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.489
\(\int \frac{1}{x \sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.490
\(\int \frac{1}{x^2 \sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.491
\(\int \frac{1}{x^3 \sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.492
\(\int x^3 \left (a+b \sqrt{c+d x}\right )^p \, dx\)
3.493
\(\int x^2 \left (a+b \sqrt{c+d x}\right )^p \, dx\)
3.494
\(\int x \left (a+b \sqrt{c+d x}\right )^p \, dx\)
3.495
\(\int \left (a+b \sqrt{c+d x}\right )^p \, dx\)
3.496
\(\int \frac{\left (a+b \sqrt{c+d x}\right )^p}{x} \, dx\)
3.497
\(\int \frac{\left (a+b (c x)^n\right )^{5/2}}{x} \, dx\)
3.498
\(\int \frac{\left (a+b (c x)^n\right )^{3/2}}{x} \, dx\)
3.499
\(\int \frac{\sqrt{a+b (c x)^n}}{x} \, dx\)
3.500
\(\int \frac{1}{x \sqrt{a+b (c x)^n}} \, dx\)
3.501
\(\int \frac{1}{x \left (a+b (c x)^n\right )^{3/2}} \, dx\)
3.502
\(\int \frac{1}{x \left (a+b (c x)^n\right )^{5/2}} \, dx\)
3.503
\(\int \frac{\left (-a+b (c x)^n\right )^{5/2}}{x} \, dx\)
3.504
\(\int \frac{\left (-a+b (c x)^n\right )^{3/2}}{x} \, dx\)
3.505
\(\int \frac{\sqrt{-a+b (c x)^n}}{x} \, dx\)
3.506
\(\int \frac{1}{x \sqrt{-a+b (c x)^n}} \, dx\)
3.507
\(\int \frac{1}{x \left (-a+b (c x)^n\right )^{3/2}} \, dx\)
3.508
\(\int \frac{1}{x \left (-a+b (c x)^n\right )^{5/2}} \, dx\)
3.509
\(\int \frac{1}{x \sqrt{a+b x}} \, dx\)
3.510
\(\int \frac{1}{x \sqrt{a+b (c x)^m}} \, dx\)
3.511
\(\int \frac{1}{x \sqrt{a+b \left (c (d x)^m\right )^n}} \, dx\)
3.512
\(\int \frac{1}{x \sqrt{a+b \left (c \left (d (e x)^m\right )^n\right )^p}} \, dx\)
3.513
\(\int \frac{1}{x \sqrt{a+b \left (c \left (d \left (e (f x)^m\right )^n\right )^p\right )^q}} \, dx\)
3.514
\(\int \frac{\sqrt{-1+\frac{1}{x^2}} \left (-1+x^2\right )^3}{x} \, dx\)
3.515
\(\int \frac{\sqrt{-1+\frac{1}{x^2}} \left (-1+x^2\right )^2}{x} \, dx\)
3.516
\(\int \frac{\sqrt{-1+\frac{1}{x^2}} \left (-1+x^2\right )}{x} \, dx\)
3.517
\(\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x \left (-1+x^2\right )} \, dx\)
3.518
\(\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x \left (-1+x^2\right )^2} \, dx\)
3.519
\(\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x \left (-1+x^2\right )^3} \, dx\)
3.520
\(\int \frac{\sqrt{1+\frac{1}{x^2}} x}{\left (1+x^2\right )^2} \, dx\)
3.521
\(\int \frac{1}{\sqrt{1+\frac{1}{x^2}} x \left (1+x^2\right )} \, dx\)
3.522
\(\int \frac{x}{a+b x^2+\sqrt{a+b x^2}} \, dx\)
3.523
\(\int \frac{x}{x^2-\sqrt [3]{x^2}} \, dx\)
3.524
\(\int x \left (1+x^2\right )^3 \sqrt{2+2 x^2+x^4} \, dx\)
3.525
\(\int x \sqrt{\frac{1-x^2}{1+x^2}} \, dx\)
3.526
\(\int x \sqrt{\frac{5-7 x^2}{7+5 x^2}} \, dx\)
3.527
\(\int x^2 \sqrt{\frac{1-x^3}{1+x^3}} \, dx\)
3.528
\(\int x^5 \sqrt{1-x^3} \left (1+x^9\right )^2 \, dx\)
3.529
\(\int x^8 \sqrt{\frac{1-x^3}{1+x^3}} \, dx\)
3.530
\(\int x^9 \sqrt{\frac{5-7 x^5}{7+5 x^5}} \, dx\)
3.531
\(\int \left (\frac{x}{\left (a+b x^2\right )^{3/2}}+\frac{x}{\left (1+x^2\right ) \sqrt{a+b x^2}}\right ) \, dx\)
3.532
\(\int \frac{x \left (1+a+x^2+b x^2\right )}{\left (1+x^2\right ) \left (a+b x^2\right )^{3/2}} \, dx\)
3.533
\(\int \left (\frac{x}{\left (a+b x^2\right )^{5/2}}+\frac{x}{\left (a+b x^2\right )^{3/2}}+\frac{x}{\left (1+x^2\right ) \sqrt{a+b x^2}}\right ) \, dx\)
3.534
\(\int \frac{x \left (1+a+a^2+x^2+a x^2+b x^2+2 a b x^2+b x^4+b^2 x^4\right )}{\left (1+x^2\right ) \left (a+b x^2\right )^{5/2}} \, dx\)
3.535
\(\int \frac{1}{\sqrt{\sqrt{x}+x}} \, dx\)
3.536
\(\int \sqrt{\sqrt{x}+x} \, dx\)
3.537
\(\int \sqrt{-x} \left (\sqrt{-x}+x\right ) \, dx\)
3.538
\(\int \frac{5+\sqrt [4]{x}}{-6+x} \, dx\)
3.539
\(\int \frac{1}{4+\sqrt{4-x}-x} \, dx\)
3.540
\(\int \frac{1}{1+x-\sqrt{2+x}} \, dx\)
3.541
\(\int \frac{1}{4+x+\sqrt{1+x}} \, dx\)
3.542
\(\int \frac{1}{x-\sqrt{1+x}} \, dx\)
3.543
\(\int \frac{1}{x-\sqrt{2+x}} \, dx\)
3.544
\(\int \frac{1}{-\sqrt{1-x}+x} \, dx\)
3.545
\(\int \sqrt{1+\sqrt{x}+x} \, dx\)
3.546
\(\int \sqrt{1+x+\sqrt{1+x}} \, dx\)
3.547
\(\int \sqrt{\sqrt{-1+x}+x} \, dx\)
3.548
\(\int \sqrt{2 x+\sqrt{-1+2 x}} \, dx\)
3.549
\(\int \sqrt{3 x+\sqrt{-7+8 x}} \, dx\)
3.550
\(\int \frac{1}{\sqrt{x+\sqrt{1+x}}} \, dx\)
3.551
\(\int \frac{1+x}{4+x+\sqrt{-9+6 x}} \, dx\)
3.552
\(\int \frac{12-x}{4+x+\sqrt{-9+6 x}} \, dx\)
3.553
\(\int \frac{-1+x^3}{\sqrt{x} \left (1+x^2\right )} \, dx\)
3.554
\(\int \frac{1}{2 \sqrt{-1+x} \sqrt{-\sqrt{-1+x}+x}} \, dx\)
3.555
\(\int \frac{1+x^{7/2}}{1-x^2} \, dx\)
3.556
\(\int \frac{4+2 x}{\sqrt [3]{-1+2 x}+\sqrt{-1+2 x}} \, dx\)
3.557
\(\int \frac{1}{\sqrt{2+\sqrt{1+\sqrt{x}}}} \, dx\)
3.558
\(\int \sqrt{2+\sqrt{4+\sqrt{x}}} \, dx\)
3.559
\(\int \sqrt{2-\sqrt{4+\sqrt{-9+5 x}}} \, dx\)
3.560
\(\int \frac{1}{\sqrt{2+\sqrt{1+\sqrt{x}}}} \, dx\)
3.561
\(\int \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{x}}}} \, dx\)
3.562
\(\int \sqrt{2+\sqrt{3+\sqrt{-1+2 \sqrt{x}}}} \, dx\)
3.563
\(\int \sqrt{1+\sqrt{1+\sqrt{-1+x}}} x \, dx\)
3.564
\(\int \frac{1}{\sqrt{-1+x} \sqrt{-\sqrt{-1+x}+x}} \, dx\)
3.565
\(\int \frac{1}{\sqrt{1+x+\sqrt{-1+2 x}}} \, dx\)
3.566
\(\int \frac{q+p x}{\sqrt{b+a x} \left (f+\sqrt{b+a x}\right )} \, dx\)
3.567
\(\int \sqrt{1-\sqrt{x}-x} \, dx\)
3.568
\(\int \frac{9+6 \sqrt{x}+x}{4 \sqrt{x}+x} \, dx\)
3.569
\(\int \frac{6-8 x^{7/2}}{5-9 \sqrt{x}} \, dx\)
3.570
\(\int \frac{\sqrt{1+x} \left (1+x^3\right )}{1+x^2} \, dx\)
3.571
\(\int \frac{\sqrt{-1-\sqrt{x}+x}}{(-1+x) \sqrt{x}} \, dx\)
3.572
\(\int \frac{1+2 \sqrt{1+x}}{x \sqrt{1+x} \sqrt{x+\sqrt{1+x}}} \, dx\)
3.573
\(\int \frac{1}{\sqrt{x} \sqrt{1+x}} \, dx\)
3.574
\(\int \frac{\sqrt{\frac{x}{1+x}}}{x} \, dx\)
3.575
\(\int \frac{\sqrt{x}}{\sqrt{1+x}} \, dx\)
3.576
\(\int \sqrt{\frac{x}{1+x}} \, dx\)
3.577
\(\int \frac{\sqrt{-1+x}}{x^2 \sqrt{1+x}} \, dx\)
3.578
\(\int \frac{\sqrt{\frac{-1+x}{1+x}}}{x^2} \, dx\)
3.579
\(\int \frac{\sqrt{-1+x} x^3}{\sqrt{1+x}} \, dx\)
3.580
\(\int x^3 \sqrt{\frac{-1+x}{1+x}} \, dx\)
3.581
\(\int \frac{\sqrt{-\frac{x}{1+x}}}{x} \, dx\)
3.582
\(\int \frac{\sqrt{\frac{1-x}{1+x}}}{-1+x} \, dx\)
3.583
\(\int \frac{\sqrt{\frac{a+b x}{c-b x}}}{a+b x} \, dx\)
3.584
\(\int \frac{\sqrt{\frac{a+b x}{c+d x}}}{a+b x} \, dx\)
3.585
\(\int \sqrt{-\frac{x}{1+x}} \, dx\)
3.586
\(\int \sqrt{\frac{1-x}{1+x}} \, dx\)
3.587
\(\int \sqrt{\frac{a+x}{a-x}} \, dx\)
3.588
\(\int \sqrt{\frac{-a+x}{a+x}} \, dx\)
3.589
\(\int \sqrt{\frac{a+b x}{c+d x}} \, dx\)
3.590
\(\int \sqrt{\frac{-1+x}{5+3 x}} \, dx\)
3.591
\(\int \frac{\sqrt{\frac{-1+5 x}{1+7 x}}}{x^2} \, dx\)
3.592
\(\int \frac{x}{\sqrt{\frac{1-x}{1+x}} (1+x)} \, dx\)
3.593
\(\int \frac{x}{(1+x) \sqrt{-1+\frac{2}{1+x}}} \, dx\)
3.594
\(\int \frac{x}{(1+x) \sqrt{\frac{2+x}{3+x}}} \, dx\)
3.595
\(\int \frac{\sqrt{1+\frac{1}{x}}}{(1+x)^2} \, dx\)
3.596
\(\int \frac{\sqrt{1+\frac{1}{x}}}{\sqrt{1-x^2}} \, dx\)
3.597
\(\int \frac{1}{x+\sqrt{3-2 x-x^2}} \, dx\)
3.598
\(\int \frac{1}{\left (x+\sqrt{3-2 x-x^2}\right )^2} \, dx\)
3.599
\(\int \frac{1}{\left (x+\sqrt{3-2 x-x^2}\right )^3} \, dx\)
3.600
\(\int \frac{1}{x+\sqrt{-3-2 x+x^2}} \, dx\)
3.601
\(\int \frac{1}{\left (x+\sqrt{-3-2 x+x^2}\right )^2} \, dx\)
3.602
\(\int \frac{1}{\left (x+\sqrt{-3-2 x+x^2}\right )^3} \, dx\)
3.603
\(\int \frac{1}{x+\sqrt{-3-4 x-x^2}} \, dx\)
3.604
\(\int \frac{1}{\left (x+\sqrt{-3-4 x-x^2}\right )^2} \, dx\)
3.605
\(\int \frac{1}{\left (x+\sqrt{-3-4 x-x^2}\right )^3} \, dx\)
3.606
\(\int x^3 (1+x)^3 (1+2 x) \sqrt{1-x^2-2 x^3-x^4} \, dx\)
3.607
\(\int (1+2 x) \left (x+x^2\right )^3 \sqrt{1-\left (x+x^2\right )^2} \, dx\)
3.608
\(\int \left (8 x-8 x^2+4 x^3-x^4\right )^{3/2} \, dx\)
3.609
\(\int \sqrt{8 x-8 x^2+4 x^3-x^4} \, dx\)
3.610
\(\int \frac{1}{\sqrt{8 x-8 x^2+4 x^3-x^4}} \, dx\)
3.611
\(\int \frac{1}{\left (8 x-8 x^2+4 x^3-x^4\right )^{3/2}} \, dx\)
3.612
\(\int \frac{1}{\left (8 x-8 x^2+4 x^3-x^4\right )^{5/2}} \, dx\)
3.613
\(\int \left ((2-x) x \left (4-2 x+x^2\right )\right )^{3/2} \, dx\)
3.614
\(\int \sqrt{(2-x) x \left (4-2 x+x^2\right )} \, dx\)
3.615
\(\int \frac{1}{\sqrt{(2-x) x \left (4-2 x+x^2\right )}} \, dx\)
3.616
\(\int \frac{1}{\left ((2-x) x \left (4-2 x+x^2\right )\right )^{3/2}} \, dx\)
3.617
\(\int \frac{1}{\left ((2-x) x \left (4-2 x+x^2\right )\right )^{5/2}} \, dx\)
3.618
\(\int \left (4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right )^{3/2} \, dx\)
3.619
\(\int \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4} \, dx\)
3.620
\(\int \frac{1}{\sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}} \, dx\)
3.621
\(\int \frac{1}{\left (4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right )^{3/2}} \, dx\)
3.622
\(\int \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4} \, dx\)
3.623
\(\int \frac{1}{\sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}} \, dx\)
3.624
\(\int \frac{1}{\left (8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right )^{3/2}} \, dx\)
3.625
\(\int \left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2} \, dx\)
3.626
\(\int \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx\)
3.627
\(\int \frac{1}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx\)
3.628
\(\int \frac{1}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2}} \, dx\)
3.629
\(\int \frac{1}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{5/2}} \, dx\)
3.630
\(\int x \left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2} \, dx\)
3.631
\(\int x \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx\)
3.632
\(\int \frac{x}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx\)
3.633
\(\int \frac{x}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2}} \, dx\)
3.634
\(\int \frac{x}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{5/2}} \, dx\)
3.635
\(\int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2} \, dx\)
3.636
\(\int x^2 \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx\)
3.637
\(\int \frac{x^2}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx\)
3.638
\(\int \frac{x^2}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2}} \, dx\)
3.639
\(\int \frac{x^2}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{5/2}} \, dx\)
3.640
\(\int \frac{1}{\sqrt{8+8 x-x^3+8 x^4}} \, dx\)
3.641
\(\int \frac{1}{\left (8+8 x-x^3+8 x^4\right )^{3/2}} \, dx\)
3.642
\(\int \frac{1}{\sqrt{1+4 x+4 x^2+4 x^4}} \, dx\)
3.643
\(\int \frac{1}{\left (1+4 x+4 x^2+4 x^4\right )^{3/2}} \, dx\)
3.644
\(\int \frac{1}{\sqrt{8+24 x+8 x^2-15 x^3+8 x^4}} \, dx\)
3.645
\(\int \frac{1}{\left (8+24 x+8 x^2-15 x^3+8 x^4\right )^{3/2}} \, dx\)
3.646
\(\int \frac{1}{\left (8+24 x+8 x^2-15 x^3+8 x^4\right )^{5/2}} \, dx\)
3.647
\(\int \frac{1}{\sqrt{9-6 x-44 x^2+15 x^3+3 x^4}} \, dx\)
3.648
\(\int \frac{1}{\left (9-6 x-44 x^2+15 x^3+3 x^4\right )^{3/2}} \, dx\)
3.649
\(\int \frac{\left (2 \sqrt{3-x}+\frac{3}{\sqrt{1+x}}\right )^2}{x} \, dx\)
3.650
\(\int \frac{-1+x+x^2}{1+\sqrt{1+x^2}} \, dx\)
3.651
\(\int \frac{-1+x+x^2}{1+x+\sqrt{1+x^2}} \, dx\)
3.652
\(\int \frac{2 \sqrt{-1+x}+x}{\sqrt{-1+x} x} \, dx\)
3.653
\(\int \left (a+c \sqrt{x}+b x^{2/3}\right )^2 \, dx\)
3.654
\(\int \left (a+c \sqrt{x}+b x^{2/3}\right )^3 \, dx\)
3.655
\(\int \frac{-1+x^2}{\sqrt{a-b+\frac{b}{x^2}} x^3} \, dx\)
3.656
\(\int \frac{-1+x^2}{\sqrt{a+b \left (-1+\frac{1}{x^2}\right )} x^3} \, dx\)
3.657
\(\int \frac{1+x}{\left (4+x^2\right ) \sqrt{9+x^2}} \, dx\)
3.658
\(\int x \left (1+\sqrt{1-x^2}\right ) \, dx\)
3.659
\(\int x \left (1+\sqrt{1-x} \sqrt{1+x}\right ) \, dx\)
3.660
\(\int x \left (1+\frac{1}{\sqrt{2+x} \sqrt{3+x}}\right ) \, dx\)
3.661
\(\int \frac{x-\sqrt{x^6}}{x \left (1-x^4\right )} \, dx\)
3.662
\(\int \frac{1-\frac{\sqrt{x^6}}{x}}{1-x^4} \, dx\)
3.663
\(\int \frac{x-\sqrt{x^6}}{x-x^5} \, dx\)
3.664
\(\int \frac{x}{x+\sqrt{x^6}} \, dx\)
3.665
\(\int \frac{\sqrt{x}-\sqrt{x^3}}{x-x^3} \, dx\)
3.666
\(\int \frac{1}{\sqrt{x}+\sqrt{x^3}} \, dx\)
3.667
\(\int \frac{1}{\sqrt{-1+x}+\sqrt{(-1+x)^3}} \, dx\)
3.668
\(\int \left (-\frac{3}{(4+5 x)^2}-\frac{5+4 x}{(4+5 x)^2 \sqrt{1-x^2}}\right ) \, dx\)
3.669
\(\int \frac{-5-4 x-3 \sqrt{1-x^2}}{(4+5 x)^2 \sqrt{1-x^2}} \, dx\)
3.670
\(\int \frac{1}{(-5-4 x) \sqrt{1-x^2}+3 \left (1-x^2\right )} \, dx\)
3.671
\(\int \frac{1}{3-3 x^2-5 \sqrt{1-x^2}-4 x \sqrt{1-x^2}} \, dx\)
3.672
\(\int \frac{-1+\sqrt{1-x^2}}{\sqrt{1-x^2} \left (2+x-2 \sqrt{1-x^2}\right )^2} \, dx\)
3.673
\(\int \frac{a+b x^{-1+n}}{c x+d x^n} \, dx\)
3.674
\(\int \frac{\sqrt{1+2 x^2}}{1+\sqrt{1+2 x^2}} \, dx\)
3.675
\(\int \frac{\sqrt{-1+4 x^2}}{x+\sqrt{-1+4 x^2}} \, dx\)
3.676
\(\int \frac{a+b x+c x^2}{(d+e x)^3 \sqrt{-1+x^2}} \, dx\)
3.677
\(\int \frac{1+2 x^8}{x \left (1+x^8\right )^{3/2}} \, dx\)
3.678
\(\int \frac{\sqrt{1+x^8} \left (1+2 x^8\right )}{x+2 x^9+x^{17}} \, dx\)
3.679
\(\int \left (1-9 x^2+\frac{x}{\sqrt{1-9 x^2}}\right ) \, dx\)
3.680
\(\int \frac{x+\left (1-9 x^2\right )^{3/2}}{\sqrt{1-9 x^2}} \, dx\)
3.681
\(\int \frac{\left (-3+2 \sqrt{x}\right ) \left (-3 \sqrt{x}+x\right )^{2/3}}{\sqrt{x}} \, dx\)
3.682
\(\int \frac{9-9 \sqrt{x}+2 x}{\sqrt [3]{-3 \sqrt{x}+x}} \, dx\)
3.683
\(\int \frac{1}{\sqrt{4-9 x^2}} \, dx\)
3.684
\(\int \frac{1}{\sqrt{2-3 x} \sqrt{2+3 x}} \, dx\)
3.685
\(\int \frac{1}{\sqrt{(2-3 x) (2+3 x)}} \, dx\)
3.686
\(\int \frac{1}{\sqrt{15-2 x-x^2}} \, dx\)
3.687
\(\int \frac{1}{\sqrt{3-x} \sqrt{5+x}} \, dx\)
3.688
\(\int \frac{1}{\sqrt{(3-x) (5+x)}} \, dx\)
3.689
\(\int \frac{1}{\sqrt{-15-8 x-x^2}} \, dx\)
3.690
\(\int \frac{1}{\sqrt{-3-x} \sqrt{5+x}} \, dx\)
3.691
\(\int \frac{1}{\sqrt{(-3-x) (5+x)}} \, dx\)
3.692
\(\int \left (1-\sqrt{x}\right ) \, dx\)
3.693
\(\int \frac{1-x}{1+\sqrt{x}} \, dx\)
3.694
\(\int \sqrt{\frac{1}{1-x^2}} \, dx\)
3.695
\(\int \sqrt{\frac{1+x^2}{1-x^4}} \, dx\)
3.696
\(\int \sqrt{\frac{1}{-1+x^2}} \, dx\)
3.697
\(\int \sqrt{\frac{1+x^2}{-1+x^4}} \, dx\)
3.698
\(\int \frac{1}{\sqrt{1-x}} \, dx\)
3.699
\(\int \frac{\sqrt{1+x}}{\sqrt{1-x^2}} \, dx\)
3.700
\(\int \frac{1}{\sqrt{1+x}} \, dx\)
3.701
\(\int \frac{\sqrt{1-x}}{\sqrt{1-x^2}} \, dx\)
3.702
\(\int \sqrt{1-x} \, dx\)
3.703
\(\int \frac{\sqrt{1-x^2}}{\sqrt{1+x}} \, dx\)
3.704
\(\int \sqrt{1+x} \, dx\)
3.705
\(\int \frac{\sqrt{1-x^2}}{\sqrt{1-x}} \, dx\)
3.706
\(\int \frac{\sqrt{2+3 x}}{\sqrt{1+x}} \, dx\)
3.707
\(\int \frac{\sqrt{1-x} \sqrt{2+3 x}}{\sqrt{1-x^2}} \, dx\)
3.708
\(\int \frac{(1+x)^{3/2}}{(1-x)^{3/2} x} \, dx\)
3.709
\(\int \frac{(1+x)^3}{x \left (1-x^2\right )^{3/2}} \, dx\)
3.710
\(\int \frac{(1+a x)^{3/2}}{x (1-a x)^{3/2}} \, dx\)
3.711
\(\int \frac{(1+a x)^3}{x \left (1-a^2 x^2\right )^{3/2}} \, dx\)
3.712
\(\int \frac{1}{\sqrt{1-x^2}} \, dx\)
3.713
\(\int \frac{\sqrt{1+x^2}}{\sqrt{1-x^4}} \, dx\)
3.714
\(\int \frac{1}{\sqrt{1+x^2}} \, dx\)
3.715
\(\int \frac{\sqrt{1-x^2}}{\sqrt{1-x^4}} \, dx\)
3.716
\(\int \sqrt{1-x^2} \, dx\)
3.717
\(\int \frac{\sqrt{1-x^4}}{\sqrt{1+x^2}} \, dx\)
3.718
\(\int \sqrt{1+x^2} \, dx\)
3.719
\(\int \frac{\sqrt{1-x^4}}{\sqrt{1-x^2}} \, dx\)
3.720
\(\int \left (\frac{a+b+c x^2}{d}\right )^m \, dx\)
3.721
\(\int \frac{1}{x-\sqrt{1+x^2}} \, dx\)
3.722
\(\int \frac{1}{x-\sqrt{1-x^2}} \, dx\)
3.723
\(\int \frac{1}{x-\sqrt{1+2 x^2}} \, dx\)
3.724
\(\int \frac{2 x-x^3+x^2 \sqrt{2-x^2}}{-2+2 x^2} \, dx\)
3.725
\(\int \frac{x \sqrt{2-x^2}}{x-\sqrt{2-x^2}} \, dx\)
3.726
\(\int \frac{x}{-x+\sqrt{2 x-x^2}} \, dx\)
3.727
\(\int \frac{x+\sqrt{2 x-x^2}}{2-2 x} \, dx\)
3.728
\(\int \frac{\sqrt{2-x} \sqrt{x}+x}{2-2 x} \, dx\)
3.729
\(\int \frac{\sqrt{x}}{\sqrt{2-x}-\sqrt{x}} \, dx\)
3.730
\(\int \frac{\sqrt{\frac{x^2}{-1+x^2}}}{1+x^2} \, dx\)
3.731
\(\int \frac{\sqrt{\frac{x^2}{-1+a+(1+a) x^2}}}{1+x^2} \, dx\)
3.732
\(\int \frac{1}{\left ((1+x) \left (-1+x^2\right )\right )^{2/3}} \, dx\)
3.733
\(\int \frac{-1+x^2}{\left (1+x^2\right ) \sqrt{x \left (1+x^2\right )}} \, dx\)
3.734
\(\int \frac{-1+x^2}{\left (1+x^2\right ) \sqrt{x+x^3}} \, dx\)
3.735
\(\int \frac{\sqrt{\frac{\left (-1+x^2\right )^2}{x \left (1+x^2\right )}}}{1+x^2} \, dx\)
3.736
\(\int \frac{\sqrt{\frac{\left (-1+x^2\right )^2}{x+x^3}}}{1+x^2} \, dx\)
3.737
\(\int \frac{1}{\sqrt{a+\frac{b}{x^2}} \sqrt{c+d x^2}} \, dx\)
3.738
\(\int \frac{\sqrt{-2 x^2+x^4}}{\left (-1+x^2\right ) \left (2+x^2\right )} \, dx\)
3.739
\(\int \frac{\sqrt{1-\frac{1}{\left (-1+x^2\right )^2}}}{2-x^2} \, dx\)
3.740
\(\int \frac{\sqrt{\frac{-2 x^2+x^4}{\left (-1+x^2\right )^2}}}{2+x^2} \, dx\)
3.741
\(\int \left (1+\frac{2 x}{1+x^2}\right )^{5/2} \, dx\)
3.742
\(\int \left (1+\frac{2 x}{1+x^2}\right )^{3/2} \, dx\)
3.743
\(\int \sqrt{1+\frac{2 x}{1+x^2}} \, dx\)
3.744
\(\int \frac{1}{\sqrt{1+\frac{2 x}{1+x^2}}} \, dx\)
3.745
\(\int \frac{1}{\left (1+\frac{2 x}{1+x^2}\right )^{3/2}} \, dx\)
3.746
\(\int \frac{\sqrt{1+\frac{2 x}{1+x^2}}}{1+x^2} \, dx\)
3.747
\(\int x^2 \left (\frac{c}{a+b x^2}\right )^{3/2} \, dx\)
3.748
\(\int x \left (\frac{c}{a+b x^2}\right )^{3/2} \, dx\)
3.749
\(\int \left (\frac{c}{a+b x^2}\right )^{3/2} \, dx\)
3.750
\(\int \frac{\left (\frac{c}{a+b x^2}\right )^{3/2}}{x} \, dx\)
3.751
\(\int \frac{\left (\frac{c}{a+b x^2}\right )^{3/2}}{x^2} \, dx\)
3.752
\(\int \frac{\left (\frac{c}{a+b x^2}\right )^{3/2}}{x^3} \, dx\)
3.753
\(\int x^2 \left (c \left (a+b x^2\right )^3\right )^{3/2} \, dx\)
3.754
\(\int x \left (c \left (a+b x^2\right )^3\right )^{3/2} \, dx\)
3.755
\(\int \left (c \left (a+b x^2\right )^3\right )^{3/2} \, dx\)
3.756
\(\int \frac{\left (c \left (a+b x^2\right )^3\right )^{3/2}}{x} \, dx\)
3.757
\(\int \frac{\left (c \left (a+b x^2\right )^3\right )^{3/2}}{x^2} \, dx\)
3.758
\(\int \frac{\left (c \left (a+b x^2\right )^3\right )^{3/2}}{x^3} \, dx\)
3.759
\(\int \sqrt{x-x^2} F(x) \, dx\)
3.760
\(\int \frac{F(x)}{\sqrt{x-x^2}} \, dx\)
3.761
\(\int \sqrt{1-x} \sqrt{x} F(x) \, dx\)
3.762
\(\int \frac{F(x)}{\sqrt{1-x} \sqrt{x}} \, dx\)
3.763
\(\int f\left (\frac{a+b x}{x}\right ) \, dx\)
3.764
\(\int f\left (\frac{a+b x^2}{x^2}\right ) \, dx\)
3.765
\(\int f\left (\frac{x}{a+b x}\right ) \, dx\)
3.766
\(\int f\left (\frac{x^2}{a+b x^2}\right ) \, dx\)
3.767
\(\int f\left (\frac{x^2}{(a+b x)^2}\right ) \, dx\)
3.768
\(\int f\left (\frac{x^4}{\left (a+b x^2\right )^2}\right ) \, dx\)
3.769
\(\int \frac{\sqrt{b x^2+\sqrt{a+b^2 x^4}}}{\sqrt{a+b^2 x^4}} \, dx\)
3.770
\(\int \frac{\sqrt{-b x^2+\sqrt{a+b^2 x^4}}}{\sqrt{a+b^2 x^4}} \, dx\)
3.771
\(\int \frac{\sqrt{2 x^2+\sqrt{3+4 x^4}}}{(c+d x) \sqrt{3+4 x^4}} \, dx\)
3.772
\(\int \frac{\sqrt{2 x^2+\sqrt{3+4 x^4}}}{(c+d x)^2 \sqrt{3+4 x^4}} \, dx\)
3.773
\(\int \frac{-4+x}{\left (1+\sqrt [3]{x}\right ) \sqrt{x}} \, dx\)
3.774
\(\int \frac{1+\sqrt{x}}{x^{5/6}+x^{7/6}} \, dx\)
3.775
\(\int \frac{1+\sqrt{x}}{\left (1+\sqrt [3]{x}\right ) \sqrt{x}} \, dx\)
3.776
\(\int \frac{\sqrt{2+\frac{b}{x^2}}}{b+2 x^2} \, dx\)
3.777
\(\int \frac{\sqrt{2-\frac{b}{x^2}}}{-b+2 x^2} \, dx\)
3.778
\(\int \frac{\sqrt{a+\frac{c}{x^2}}}{d+e x} \, dx\)
3.779
\(\int \frac{\sqrt{a+\frac{c}{x^2}+\frac{b}{x}}}{d+e x} \, dx\)
3.780
\(\int \frac{\sqrt [6]{x}+\sqrt [5]{x^3}}{\sqrt{x}} \, dx\)
3.781
\(\int \frac{2+x}{\sqrt{4 x-x^2}} \, dx\)
3.782
\(\int \frac{3+x}{\sqrt [3]{6 x+x^2}} \, dx\)
3.783
\(\int \frac{4+x}{\left (6 x-x^2\right )^{3/2}} \, dx\)
3.784
\(\int \frac{1}{(1+x) \sqrt{2 x+x^2}} \, dx\)
3.785
\(\int \frac{1}{(1+2 x) \sqrt{x+x^2}} \, dx\)
3.786
\(\int \frac{-1+x}{\sqrt{2 x-x^2}} \, dx\)
3.787
\(\int \frac{\sqrt{x-x^2}}{1+x} \, dx\)
3.788
\(\int \sqrt{\sqrt [4]{x}+x} \, dx\)
3.789
\(\int \sqrt{x+x^{3/2}} \, dx\)
3.790
\(\int x \sqrt{x+x^{3/2}} \, dx\)
3.791
\(\int \left (1-x^2\right ) \sqrt{\frac{1}{2-x^2}} \, dx\)
3.792
\(\int \sqrt{x^2+x^3-x^4} \, dx\)
3.793
\(\int \frac{1}{\sqrt{\left (a^2+x^2\right )^3}} \, dx\)
3.794
\(\int \frac{\sqrt{x}}{1+\sqrt{x}+x} \, dx\)
3.795
\(\int \frac{x}{1+\sqrt{x}+x} \, dx\)
3.796
\(\int \frac{1}{\sqrt{x} \left (1+\sqrt{x}+x\right )^{7/2}} \, dx\)
3.797
\(\int \frac{-1+x}{1+\sqrt{1+x^2}} \, dx\)
3.798
\(\int \frac{1}{(1+x)^{2/3} \left (-1+x^2\right )^{2/3}} \, dx\)
3.799
\(\int \left (\left (1-x^6\right )^{2/3}+\frac{\left (1-x^6\right )^{2/3}}{x^6}\right ) \, dx\)
3.800
\(\int \frac{x^{-1+m} \left (2 a m+b (2 m-n) x^n\right )}{2 \left (a+b x^n\right )^{3/2}} \, dx\)
3.801
\(\int \frac{x-2 x^3}{\sqrt{2+3 x}} \, dx\)
3.802
\(\int \frac{1}{\sqrt [4]{1+x}+\sqrt{1+x}} \, dx\)
3.803
\(\int \frac{1+2 x}{\sqrt{x+x^2}} \, dx\)
3.804
\(\int \frac{1}{2 \sqrt{x} (1+x)} \, dx\)
3.805
\(\int \frac{1}{x \sqrt{6 x-x^2}} \, dx\)
3.806
\(\int \left (1+\sqrt{x}\right ) \sqrt{x} \, dx\)
3.807
\(\int \frac{1-\sqrt{x}}{\sqrt [3]{x}} \, dx\)
3.808
\(\int \frac{\sqrt{x}}{1+\sqrt [3]{x}} \, dx\)
3.809
\(\int \frac{\sqrt [3]{1+\sqrt{x}}}{x} \, dx\)
3.810
\(\int \left (1-\sqrt{x}\right ) \, dx\)
3.811
\(\int \left (1-\sqrt [4]{x}\right ) \, dx\)
3.812
\(\int \frac{1-\sqrt{x}}{1+\sqrt [4]{x}} \, dx\)
3.813
\(\int \frac{1}{\sqrt{(a+b x) (c+d x)}} \, dx\)
3.814
\(\int \frac{1}{\sqrt{(a+b x) (c-d x)}} \, dx\)
3.815
\(\int \frac{1}{\sqrt{x} \left (1-x^2\right )} \, dx\)
3.816
\(\int \frac{\sqrt{x}}{x-x^3} \, dx\)
3.817
\(\int \frac{x}{2-\sqrt{3}+\left (1+\sqrt{3}\right ) x+x^2} \, dx\)
3.818
\(\int \sqrt{x^2+x^3} \, dx\)
3.819
\(\int \frac{1}{(1+x) \sqrt{2 x+x^2}} \, dx\)
3.820
\(\int \sqrt{1-\sqrt{x}-x} \sqrt{x} \, dx\)
3.821
\(\int \sqrt [3]{1+\sqrt{-3+x}} \, dx\)
3.822
\(\int \frac{1}{\sqrt{3+\sqrt{-1+2 x}}} \, dx\)
3.823
\(\int \frac{\sqrt{1-x}}{1+\sqrt{x}} \, dx\)
3.824
\(\int \frac{\sqrt{1-x}}{1-\sqrt{x}} \, dx\)
3.825
\(\int \frac{x}{x-\sqrt{1+x^2}} \, dx\)
3.826
\(\int \frac{x}{x-\sqrt{1-x^2}} \, dx\)
3.827
\(\int \frac{x}{x-\sqrt{1+2 x^2}} \, dx\)
3.828
\(\int \sqrt{x} \sqrt{\sqrt{x}+x} \, dx\)
3.829
\(\int \frac{1+\sqrt [3]{x}}{1+\sqrt{x}} \, dx\)
3.830
\(\int \frac{1+\sqrt [3]{x}}{1+\sqrt [4]{x}} \, dx\)
3.831
\(\int \frac{x^2}{-1+x^2+\sqrt{1-x^2}} \, dx\)
3.832
\(\int \sqrt{\frac{1+x}{x}} \, dx\)
3.833
\(\int \sqrt{\frac{1-x}{x}} \, dx\)
3.834
\(\int \sqrt{\frac{-1+x}{x}} \, dx\)
3.835
\(\int \frac{\sqrt{\frac{1+x}{x}}}{x} \, dx\)
3.836
\(\int \sqrt{\frac{x}{1+x}} \, dx\)
3.837
\(\int \frac{1}{\sqrt{\frac{-1-x}{x}}} \, dx\)
3.838
\(\int \sqrt{(4-x) x} \, dx\)
3.839
\(\int \frac{1}{\sqrt{(1-x) x}} \, dx\)
3.840
\(\int \frac{x}{(x (2+x))^{3/2}} \, dx\)
3.841
\(\int \frac{\sqrt{1+\frac{1}{x}}}{1-x^2} \, dx\)
3.842
\(\int \frac{1}{1+\sqrt{5}-x^2+\sqrt{5} x^2} \, dx\)
3.843
\(\int \sqrt{(b-x) (-a+x)} \, dx\)
3.844
\(\int \frac{1}{\sqrt{(b-x) (-a+x)}} \, dx\)
3.845
\(\int \sqrt{\left (1-x^2\right ) \left (3+x^2\right )} \, dx\)
3.846
\(\int \frac{1}{\sqrt{\left (1-x^2\right ) \left (3+x^2\right )}} \, dx\)
3.847
\(\int \frac{1}{\sqrt{a x+b x^2}} \, dx\)
3.848
\(\int \frac{1}{\sqrt{x (a+b x)}} \, dx\)
3.849
\(\int \frac{1}{\sqrt{\left (b+\frac{a}{x}\right ) x^2}} \, dx\)
3.850
\(\int \frac{1}{\sqrt{\left (\frac{a}{x^2}+\frac{b}{x}\right ) x^3}} \, dx\)
3.851
\(\int \frac{1}{\sqrt{\frac{a x^2+b x^3}{x}}} \, dx\)
3.852
\(\int \frac{1}{\sqrt{\frac{a x^3+b x^4}{x^2}}} \, dx\)
3.853
\(\int \frac{1}{\sqrt{a c x+b c x^2}} \, dx\)
3.854
\(\int \frac{1}{\sqrt{c \left (a x+b x^2\right )}} \, dx\)
3.855
\(\int \frac{1}{\sqrt{c x (a+b x)}} \, dx\)
3.856
\(\int \frac{1}{\sqrt{c \left (b+\frac{a}{x}\right ) x^2}} \, dx\)
3.857
\(\int \sqrt{1-x^2+x \sqrt{-1+x^2}} \, dx\)
3.858
\(\int \frac{\sqrt{-x+\sqrt{x} \sqrt{1+x}}}{\sqrt{1+x}} \, dx\)
3.859
\(\int -\frac{x+2 \sqrt{1+x^2}}{x+x^3+\sqrt{1+x^2}} \, dx\)
3.860
\(\int \frac{1+2 x}{\left (1+x^2\right ) \sqrt{2+2 x+x^2}} \, dx\)
3.861
\(\int \frac{1}{\left (1+x^4\right ) \sqrt{-x^2+\sqrt{1+x^4}}} \, dx\)
3.862
\(\int \frac{1}{\left (a+b x^4\right ) \sqrt{c x^2+d \sqrt{a+b x^4}}} \, dx\)
3.863
\(\int \frac{1}{\left (a+b x^4\right ) \sqrt{-c x^2+d \sqrt{a+b x^4}}} \, dx\)
3.864
\(\int \frac{x}{\sqrt{a+b c^4+4 b c^3 d x+6 b c^2 d^2 x^2+4 b c d^3 x^3+b d^4 x^4}} \, dx\)
3.865
\(\int \frac{1}{\sqrt{a+b c^4+4 b c^3 d x+6 b c^2 d^2 x^2+4 b c d^3 x^3+b d^4 x^4}} \, dx\)
3.866
\(\int \frac{a-c x^4}{\sqrt{a+b x^2+c x^4} \left (a d+a e x^2+c d x^4\right )} \, dx\)
3.867
\(\int \frac{a-c x^4}{\sqrt{a-b x^2+c x^4} \left (a d+a e x^2+c d x^4\right )} \, dx\)
3.868
\(\int \frac{1}{\sqrt{5-2 x+x^2} \left (8+x^3\right )} \, dx\)
3.869
\(\int \sqrt{\frac{x^2}{1+x^2}} \, dx\)
3.870
\(\int \sqrt{\frac{x^n}{1+x^n}} \, dx\)
3.871
\(\int \frac{e f-e f x^2}{\left (a d+b d x+a d x^2\right ) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx\)
3.872
\(\int \frac{e f-e f x^2}{\left (-a d+b d x-a d x^2\right ) \sqrt{-a+b x+c x^2+b x^3-a x^4}} \, dx\)
3.873
\(\int \frac{\sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
3.874
\(\int \frac{\sqrt{-a x^2+b x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
3.875
\(\int \frac{\sqrt{x \left (a x+b \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}\right )}}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
3.876
\(\int \frac{\sqrt{x \left (-a x+b \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}\right )}}{x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
3.877
\(\int \frac{-\sqrt{-4+x}-4 \sqrt{-1+x}+\sqrt{-4+x} x+\sqrt{-1+x} x}{\left (1+\sqrt{-4+x}+\sqrt{-1+x}\right ) \left (4-5 x+x^2\right )} \, dx\)
3.878
\(\int \frac{1}{x \left (3+3 x+x^2\right ) \sqrt [3]{3+3 x+3 x^2+x^3}} \, dx\)
3.879
\(\int \frac{1-x^2}{\left (1-x+x^2\right ) \left (1-x^3\right )^{2/3}} \, dx\)
3.880
\(\int \frac{x^2}{\sqrt{-1+x^4} \left (1+x^4\right )} \, dx\)
3.881
\(\int \frac{a-c x^4}{\left (a e+c d x^2\right ) \left (d+e x^2\right ) \sqrt{a+b x^2+c x^4}} \, dx\)
3.882
\(\int \left (x+\frac{1-x^2}{1+x}\right ) \, dx\)
3.883
\(\int \frac{1}{\frac{1}{x}+\sqrt{1-x^2}} \, dx\)
3.884
\(\int \frac{x \sqrt{1-x^2}}{x-x^3+\sqrt{1-x^2}} \, dx\)
3.885
\(\int \left (1+x+x^2+x^3\right )^{-n} \left (1-x^4\right )^n \, dx\)
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