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Chapter 3
Listing of integrals
3.1
\(\int \frac{1}{(2^{2/3}+x) \sqrt{1+x^3}} \, dx\)
3.2
\(\int \frac{1}{(2^{2/3}-x) \sqrt{1-x^3}} \, dx\)
3.3
\(\int \frac{1}{(2^{2/3}-x) \sqrt{-1+x^3}} \, dx\)
3.4
\(\int \frac{1}{(2^{2/3}+x) \sqrt{-1-x^3}} \, dx\)
3.5
\(\int \frac{1}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.6
\(\int \frac{1}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.7
\(\int \frac{1}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.8
\(\int \frac{1}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.9
\(\int \frac{1}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
3.10
\(\int \frac{1}{(1+\sqrt{3}+x) \sqrt{1+x^3}} \, dx\)
3.11
\(\int \frac{1}{(1+\sqrt{3}-x) \sqrt{1-x^3}} \, dx\)
3.12
\(\int \frac{1}{(1+\sqrt{3}-x) \sqrt{-1+x^3}} \, dx\)
3.13
\(\int \frac{1}{(1+\sqrt{3}+x) \sqrt{-1-x^3}} \, dx\)
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
\(\int \frac{1}{(c+d x) (2 c^3+d^3 x^3)^{2/3}} \, dx\)
3.21
\(\int \frac{1}{(1+\sqrt [3]{2} x) (1+x^3)^{2/3}} \, dx\)
3.22
\(\int \frac{1}{(1-\sqrt [3]{2} x) (1-x^3)^{2/3}} \, dx\)
3.23
\(\int (c+d x)^4 \sqrt [3]{a+b x^3} \, dx\)
3.24
\(\int (c+d x)^3 \sqrt [3]{a+b x^3} \, dx\)
3.25
\(\int (c+d x)^2 \sqrt [3]{a+b x^3} \, dx\)
3.26
\(\int (c+d x) \sqrt [3]{a+b x^3} \, dx\)
3.27
\(\int \frac{\sqrt [3]{a+b x^3}}{c+d x} \, dx\)
3.28
\(\int \frac{\sqrt [3]{a+b x^3}}{(c+d x)^2} \, dx\)
3.29
\(\int \frac{(c+d x)^4}{\sqrt [3]{a+b x^3}} \, dx\)
3.30
\(\int \frac{(c+d x)^3}{\sqrt [3]{a+b x^3}} \, dx\)
3.31
\(\int \frac{(c+d x)^2}{\sqrt [3]{a+b x^3}} \, dx\)
3.32
\(\int \frac{c+d x}{\sqrt [3]{a+b x^3}} \, dx\)
3.33
\(\int \frac{1}{(c+d x) \sqrt [3]{a+b x^3}} \, dx\)
3.34
\(\int \frac{1}{(c+d x)^2 \sqrt [3]{a+b x^3}} \, dx\)
3.35
\(\int \frac{1}{(c+d x)^3 \sqrt [3]{a+b x^3}} \, dx\)
3.36
\(\int \frac{(c+d x)^4}{(a+b x^3)^{2/3}} \, dx\)
3.37
\(\int \frac{(c+d x)^3}{(a+b x^3)^{2/3}} \, dx\)
3.38
\(\int \frac{(c+d x)^2}{(a+b x^3)^{2/3}} \, dx\)
3.39
\(\int \frac{c+d x}{(a+b x^3)^{2/3}} \, dx\)
3.40
\(\int \frac{1}{(c+d x) (a+b x^3)^{2/3}} \, dx\)
3.41
\(\int \frac{1}{(c+d x)^2 (a+b x^3)^{2/3}} \, dx\)
3.42
\(\int \frac{1}{(c+d x)^3 (a+b x^3)^{2/3}} \, dx\)
3.43
\(\int \frac{2^{2/3}-2 x}{(2^{2/3}+x) \sqrt{1+x^3}} \, dx\)
3.44
\(\int \frac{2^{2/3}+2 x}{(2^{2/3}-x) \sqrt{1-x^3}} \, dx\)
3.45
\(\int \frac{2^{2/3}+2 x}{(2^{2/3}-x) \sqrt{-1+x^3}} \, dx\)
3.46
\(\int \frac{2^{2/3}-2 x}{(2^{2/3}+x) \sqrt{-1-x^3}} \, dx\)
3.47
\(\int \frac{2^{2/3} \sqrt [3]{a}-2 \sqrt [3]{b} x}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.48
\(\int \frac{2^{2/3} \sqrt [3]{a}+2 \sqrt [3]{b} x}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.49
\(\int \frac{2^{2/3} \sqrt [3]{a}+2 \sqrt [3]{b} x}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.50
\(\int \frac{2^{2/3} \sqrt [3]{a}-2 \sqrt [3]{b} x}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.51
\(\int \frac{c-2 d x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
3.52
\(\int \frac{2+3 x}{(2^{2/3}+x) \sqrt{1+x^3}} \, dx\)
3.53
\(\int \frac{2+3 x}{(2^{2/3}-x) \sqrt{1-x^3}} \, dx\)
3.54
\(\int \frac{2+3 x}{(2^{2/3}-x) \sqrt{-1+x^3}} \, dx\)
3.55
\(\int \frac{2+3 x}{(2^{2/3}+x) \sqrt{-1-x^3}} \, dx\)
3.56
\(\int \frac{e+f x}{(2^{2/3}+x) \sqrt{1+x^3}} \, dx\)
3.57
\(\int \frac{e+f x}{(2^{2/3}-x) \sqrt{1-x^3}} \, dx\)
3.58
\(\int \frac{e+f x}{(2^{2/3}-x) \sqrt{-1+x^3}} \, dx\)
3.59
\(\int \frac{e+f x}{(2^{2/3}+x) \sqrt{-1-x^3}} \, dx\)
3.60
\(\int \frac{e+f x}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.61
\(\int \frac{e+f x}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.62
\(\int \frac{e+f x}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.63
\(\int \frac{e+f x}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.64
\(\int \frac{e+f x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
3.65
\(\int \frac{x}{(2^{2/3}+x) \sqrt{1+x^3}} \, dx\)
3.66
\(\int \frac{x}{(2^{2/3}-x) \sqrt{1-x^3}} \, dx\)
3.67
\(\int \frac{x}{(2^{2/3}-x) \sqrt{-1+x^3}} \, dx\)
3.68
\(\int \frac{x}{(2^{2/3}+x) \sqrt{-1-x^3}} \, dx\)
3.69
\(\int \frac{x}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.70
\(\int \frac{x}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.71
\(\int \frac{x}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.72
\(\int \frac{x}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.73
\(\int \frac{x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
3.74
\(\int \frac{1+x}{(2-x) \sqrt{1+x^3}} \, dx\)
3.75
\(\int \frac{1-x}{(2+x) \sqrt{1-x^3}} \, dx\)
3.76
\(\int \frac{1-x}{(2+x) \sqrt{-1+x^3}} \, dx\)
3.77
\(\int \frac{1+x}{(2-x) \sqrt{-1-x^3}} \, dx\)
3.78
\(\int \frac{\sqrt [3]{a}+\sqrt [3]{b} x}{(2 \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.79
\(\int \frac{\sqrt [3]{a}-\sqrt [3]{b} x}{(2 \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.80
\(\int \frac{\sqrt [3]{a}-\sqrt [3]{b} x}{(2 \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.81
\(\int \frac{\sqrt [3]{a}+\sqrt [3]{b} x}{(2 \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.82
\(\int \frac{c-2 d x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx\)
3.83
\(\int \frac{e+f x}{(2-x) \sqrt{1+x^3}} \, dx\)
3.84
\(\int \frac{e+f x}{(2+x) \sqrt{1-x^3}} \, dx\)
3.85
\(\int \frac{e+f x}{(2+x) \sqrt{-1+x^3}} \, dx\)
3.86
\(\int \frac{e+f x}{(2-x) \sqrt{-1-x^3}} \, dx\)
3.87
\(\int \frac{e+f x}{(2 \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.88
\(\int \frac{e+f x}{(2 \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.89
\(\int \frac{e+f x}{(2 \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.90
\(\int \frac{e+f x}{(2 \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.91
\(\int \frac{e+f x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx\)
3.92
\(\int \frac{x}{(2-x) \sqrt{1+x^3}} \, dx\)
3.93
\(\int \frac{x}{(2+x) \sqrt{1-x^3}} \, dx\)
3.94
\(\int \frac{x}{(2+x) \sqrt{-1+x^3}} \, dx\)
3.95
\(\int \frac{x}{(2-x) \sqrt{-1-x^3}} \, dx\)
3.96
\(\int \frac{x}{(2 \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.97
\(\int \frac{x}{(2 \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.98
\(\int \frac{x}{(2 \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.99
\(\int \frac{x}{(2 \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.100
\(\int \frac{x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx\)
3.101
\(\int \frac{1+\sqrt{3}+x}{(1-\sqrt{3}+x) \sqrt{1+x^3}} \, dx\)
3.102
\(\int \frac{1+\sqrt{3}-x}{(1-\sqrt{3}-x) \sqrt{1-x^3}} \, dx\)
3.103
\(\int \frac{1+\sqrt{3}-x}{(1-\sqrt{3}-x) \sqrt{-1+x^3}} \, dx\)
3.104
\(\int \frac{1+\sqrt{3}+x}{(1-\sqrt{3}+x) \sqrt{-1-x^3}} \, dx\)
3.105
\(\int \frac{(1+\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1-\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.106
\(\int \frac{(1+\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1-\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.107
\(\int \frac{(1+\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1-\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.108
\(\int \frac{(1+\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1-\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.109
\(\int \frac{1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{(1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x) \sqrt{a+b x^3}} \, dx\)
3.110
\(\int \frac{1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{(1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x) \sqrt{a-b x^3}} \, dx\)
3.111
\(\int \frac{1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{(1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x) \sqrt{-a+b x^3}} \, dx\)
3.112
\(\int \frac{1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{(1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x) \sqrt{-a-b x^3}} \, dx\)
3.113
\(\int \frac{1-\sqrt{3}+x}{(1+\sqrt{3}+x) \sqrt{1+x^3}} \, dx\)
3.114
\(\int \frac{1-\sqrt{3}-x}{(1+\sqrt{3}-x) \sqrt{1-x^3}} \, dx\)
3.115
\(\int \frac{1-\sqrt{3}-x}{(1+\sqrt{3}-x) \sqrt{-1+x^3}} \, dx\)
3.116
\(\int \frac{1-\sqrt{3}+x}{(1+\sqrt{3}+x) \sqrt{-1-x^3}} \, dx\)
3.117
\(\int \frac{(1-\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1+\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.118
\(\int \frac{(1-\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1+\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.119
\(\int \frac{(1-\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1+\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.120
\(\int \frac{(1-\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1+\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.121
\(\int \frac{1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{(1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x) \sqrt{a+b x^3}} \, dx\)
3.122
\(\int \frac{1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{(1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x) \sqrt{a-b x^3}} \, dx\)
3.123
\(\int \frac{1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{(1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x) \sqrt{-a+b x^3}} \, dx\)
3.124
\(\int \frac{1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{(1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x) \sqrt{-a-b x^3}} \, dx\)
3.125
\(\int \frac{1+x}{(1+\sqrt{3}+x) \sqrt{1+x^3}} \, dx\)
3.126
\(\int \frac{1+x}{(1-\sqrt{3}+x) \sqrt{1+x^3}} \, dx\)
3.127
\(\int \frac{e+f x}{(1+\sqrt{3}+x) \sqrt{1+x^3}} \, dx\)
3.128
\(\int \frac{e+f x}{(1+\sqrt{3}-x) \sqrt{1-x^3}} \, dx\)
3.129
\(\int \frac{e+f x}{(1+\sqrt{3}-x) \sqrt{-1+x^3}} \, dx\)
3.130
\(\int \frac{e+f x}{(1+\sqrt{3}+x) \sqrt{-1-x^3}} \, dx\)
3.131
\(\int \frac{e+f x}{((1-\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.132
\(\int \frac{e+f x}{((1-\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.133
\(\int \frac{e+f x}{((1-\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.134
\(\int \frac{e+f x}{((1-\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.135
\(\int \frac{x}{(1+\sqrt{3}+x) \sqrt{1+x^3}} \, dx\)
3.136
\(\int \frac{x}{(1+\sqrt{3}-x) \sqrt{1-x^3}} \, dx\)
3.137
\(\int \frac{x}{(1+\sqrt{3}-x) \sqrt{-1+x^3}} \, dx\)
3.138
\(\int \frac{x}{(1+\sqrt{3}+x) \sqrt{-1-x^3}} \, dx\)
3.139
\(\int \frac{x}{(1-\sqrt{3}+x) \sqrt{1+x^3}} \, dx\)
3.140
\(\int \frac{x}{((1-\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{a+b x^3}} \, dx\)
3.141
\(\int \frac{x}{((1-\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{a-b x^3}} \, dx\)
3.142
\(\int \frac{x}{((1-\sqrt{3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt{-a+b x^3}} \, dx\)
3.143
\(\int \frac{x}{((1-\sqrt{3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt{-a-b x^3}} \, dx\)
3.144
\(\int \frac{1+\sqrt{3}+x}{(c+d x) \sqrt{1+x^3}} \, dx\)
3.145
\(\int \frac{1+\sqrt{3}-x}{(c+d x) \sqrt{1-x^3}} \, dx\)
3.146
\(\int \frac{1+\sqrt{3}-x}{(c+d x) \sqrt{-1+x^3}} \, dx\)
3.147
\(\int \frac{1+\sqrt{3}+x}{(c+d x) \sqrt{-1-x^3}} \, dx\)
3.148
\(\int \frac{1-\sqrt{3}+x}{(c+d x) \sqrt{1+x^3}} \, dx\)
3.149
\(\int \frac{1-\sqrt{3}-x}{(c+d x) \sqrt{1-x^3}} \, dx\)
3.150
\(\int \frac{1-\sqrt{3}-x}{(c+d x) \sqrt{-1+x^3}} \, dx\)
3.151
\(\int \frac{1-\sqrt{3}+x}{(c+d x) \sqrt{-1-x^3}} \, dx\)
3.152
\(\int \frac{1+\sqrt{3}+x}{x \sqrt{1+x^3}} \, dx\)
3.153
\(\int \frac{1+\sqrt{3}-x}{x \sqrt{1-x^3}} \, dx\)
3.154
\(\int \frac{1+\sqrt{3}-x}{x \sqrt{-1+x^3}} \, dx\)
3.155
\(\int \frac{1+\sqrt{3}+x}{x \sqrt{-1-x^3}} \, dx\)
3.156
\(\int \frac{1-\sqrt{3}+x}{x \sqrt{1+x^3}} \, dx\)
3.157
\(\int \frac{1-\sqrt{3}-x}{x \sqrt{1-x^3}} \, dx\)
3.158
\(\int \frac{1-\sqrt{3}-x}{x \sqrt{-1+x^3}} \, dx\)
3.159
\(\int \frac{1-\sqrt{3}+x}{x \sqrt{-1-x^3}} \, dx\)
3.160
\(\int \frac{x}{(3+x) \sqrt{1+x^3}} \, dx\)
3.161
\(\int \frac{x}{(3+x) \sqrt{1-x^3}} \, dx\)
3.162
\(\int \frac{x}{(3+x) \sqrt{-1+x^3}} \, dx\)
3.163
\(\int \frac{x}{(3+x) \sqrt{-1-x^3}} \, dx\)
3.164
\(\int \frac{e+f x}{(c+d x) \sqrt{1+x^3}} \, dx\)
3.165
\(\int \frac{e+f x}{(c+d x) \sqrt{1-x^3}} \, dx\)
3.166
\(\int \frac{e+f x}{(c+d x) \sqrt{-1+x^3}} \, dx\)
3.167
\(\int \frac{e+f x}{(c+d x) \sqrt{-1-x^3}} \, dx\)
3.168
\(\int \frac{e+f x}{x \sqrt{1+x^3}} \, dx\)
3.169
\(\int \frac{e+f x}{x \sqrt{1-x^3}} \, dx\)
3.170
\(\int \frac{e+f x}{x \sqrt{-1+x^3}} \, dx\)
3.171
\(\int \frac{e+f x}{x \sqrt{-1-x^3}} \, dx\)
3.172
\(\int \frac{c-d x}{(c+d x) \sqrt [3]{2 c^3+d^3 x^3}} \, dx\)
3.173
\(\int \frac{e+f x}{(c+d x) \sqrt [3]{-c^3+d^3 x^3}} \, dx\)
3.174
\(\int x^2 (a+b x)^n (c+d x^3) \, dx\)
3.175
\(\int x (a+b x)^n (c+d x^3) \, dx\)
3.176
\(\int (a+b x)^n (c+d x^3) \, dx\)
3.177
\(\int \frac{(a+b x)^n (c+d x^3)}{x} \, dx\)
3.178
\(\int x^2 (a+b x)^n (c+d x^3)^2 \, dx\)
3.179
\(\int x (a+b x)^n (c+d x^3)^2 \, dx\)
3.180
\(\int (a+b x)^n (c+d x^3)^2 \, dx\)
3.181
\(\int \frac{(a+b x)^n (c+d x^3)^2}{x} \, dx\)
3.182
\(\int x^2 (a+b x)^n (c+d x^3)^3 \, dx\)
3.183
\(\int x (a+b x)^n (c+d x^3)^3 \, dx\)
3.184
\(\int (a+b x)^n (c+d x^3)^3 \, dx\)
3.185
\(\int \frac{(a+b x)^n (c+d x^3)^3}{x} \, dx\)
3.186
\(\int \frac{x^5 (e+f x)^n}{a+b x^3} \, dx\)
3.187
\(\int \frac{x^4 (e+f x)^n}{a+b x^3} \, dx\)
3.188
\(\int \frac{x^3 (e+f x)^n}{a+b x^3} \, dx\)
3.189
\(\int \frac{x^2 (e+f x)^n}{a+b x^3} \, dx\)
3.190
\(\int \frac{x (e+f x)^n}{a+b x^3} \, dx\)
3.191
\(\int \frac{(e+f x)^n}{a+b x^3} \, dx\)
3.192
\(\int \frac{(e+f x)^n}{x (a+b x^3)} \, dx\)
3.193
\(\int \frac{(e+f x)^n}{x^2 (a+b x^3)} \, dx\)
3.194
\(\int \frac{x^2 (c+d x)^{1+n}}{a+b x^3} \, dx\)
3.195
\(\int \frac{x^m (e+f x)^n}{a+b x^3} \, dx\)
3.196
\(\int \frac{\sqrt{c+d x^3}}{a+b x} \, dx\)
3.197
\(\int \frac{(d^3+e^3 x^3)^p}{d+e x} \, dx\)
3.198
\(\int \frac{2-2 x-x^2}{(2+x^2) \sqrt{1+x^3}} \, dx\)
3.199
\(\int \frac{2+2 x-x^2}{(2+x^2) \sqrt{1-x^3}} \, dx\)
3.200
\(\int \frac{2+2 x-x^2}{(2+x^2) \sqrt{-1+x^3}} \, dx\)
3.201
\(\int \frac{2-2 x-x^2}{(2+x^2) \sqrt{-1-x^3}} \, dx\)
3.202
\(\int \frac{2-2 x-x^2}{(2+d+d x+x^2) \sqrt{1+x^3}} \, dx\)
3.203
\(\int \frac{2+2 x-x^2}{(2-d+d x+x^2) \sqrt{1-x^3}} \, dx\)
3.204
\(\int \frac{2+2 x-x^2}{(2-d+d x+x^2) \sqrt{-1+x^3}} \, dx\)
3.205
\(\int \frac{2-2 x-x^2}{(2+d+d x+x^2) \sqrt{-1-x^3}} \, dx\)
3.206
\(\int (d+e x)^3 \sqrt{a+c x^4} \, dx\)
3.207
\(\int (d+e x)^2 \sqrt{a+c x^4} \, dx\)
3.208
\(\int (d+e x) \sqrt{a+c x^4} \, dx\)
3.209
\(\int \sqrt{a+c x^4} \, dx\)
3.210
\(\int \frac{\sqrt{a+c x^4}}{d+e x} \, dx\)
3.211
\(\int \frac{\sqrt{a+c x^4}}{(d+e x)^2} \, dx\)
3.212
\(\int \frac{(d+e x)^3}{\sqrt{a+c x^4}} \, dx\)
3.213
\(\int \frac{(d+e x)^2}{\sqrt{a+c x^4}} \, dx\)
3.214
\(\int \frac{d+e x}{\sqrt{a+c x^4}} \, dx\)
3.215
\(\int \frac{1}{\sqrt{a+c x^4}} \, dx\)
3.216
\(\int \frac{1}{(d+e x) \sqrt{a+c x^4}} \, dx\)
3.217
\(\int \frac{1}{(d+e x)^2 \sqrt{a+c x^4}} \, dx\)
3.218
\(\int \frac{1}{(d+e x)^3 \sqrt{a+c x^4}} \, dx\)
3.219
\(\int \frac{(d+e x)^3}{(a+c x^4)^{3/2}} \, dx\)
3.220
\(\int \frac{(d+e x)^2}{(a+c x^4)^{3/2}} \, dx\)
3.221
\(\int \frac{d+e x}{(a+c x^4)^{3/2}} \, dx\)
3.222
\(\int \frac{1}{(a+c x^4)^{3/2}} \, dx\)
3.223
\(\int \frac{1}{(d+e x) (a+c x^4)^{3/2}} \, dx\)
3.224
\(\int \frac{x^3 (c+d x)^n}{a+b x^4} \, dx\)
3.225
\(\int \frac{x^3 (c+d x)^{1+n}}{a+b x^4} \, dx\)
3.226
\(\int \frac{1}{(c+d x+e x^2) \sqrt{a+b x^4}} \, dx\)
3.227
\(\int x^m (c (a+b x^2)^2)^{3/2} \, dx\)
3.228
\(\int x^5 (c (a+b x^2)^2)^{3/2} \, dx\)
3.229
\(\int x^4 (c (a+b x^2)^2)^{3/2} \, dx\)
3.230
\(\int x^3 (c (a+b x^2)^2)^{3/2} \, dx\)
3.231
\(\int x^2 (c (a+b x^2)^2)^{3/2} \, dx\)
3.232
\(\int x (c (a+b x^2)^2)^{3/2} \, dx\)
3.233
\(\int (c (a+b x^2)^2)^{3/2} \, dx\)
3.234
\(\int \frac{(c (a+b x^2)^2)^{3/2}}{x} \, dx\)
3.235
\(\int \frac{(c (a+b x^2)^2)^{3/2}}{x^2} \, dx\)
3.236
\(\int \frac{(c (a+b x^2)^2)^{3/2}}{x^3} \, dx\)
3.237
\(\int x^2 (c (a+b x^2)^3)^{3/2} \, dx\)
3.238
\(\int x (c (a+b x^2)^3)^{3/2} \, dx\)
3.239
\(\int (c (a+b x^2)^3)^{3/2} \, dx\)
3.240
\(\int \frac{(c (a+b x^2)^3)^{3/2}}{x} \, dx\)
3.241
\(\int \frac{(c (a+b x^2)^3)^{3/2}}{x^2} \, dx\)
3.242
\(\int \frac{(c (a+b x^2)^3)^{3/2}}{x^3} \, dx\)
3.243
\(\int x^2 (\frac{c}{a+b x^2})^{3/2} \, dx\)
3.244
\(\int x (\frac{c}{a+b x^2})^{3/2} \, dx\)
3.245
\(\int (\frac{c}{a+b x^2})^{3/2} \, dx\)
3.246
\(\int \frac{(\frac{c}{a+b x^2})^{3/2}}{x} \, dx\)
3.247
\(\int \frac{(\frac{c}{a+b x^2})^{3/2}}{x^2} \, dx\)
3.248
\(\int \frac{(\frac{c}{a+b x^2})^{3/2}}{x^3} \, dx\)
3.249
\(\int x^7 (c \sqrt{a+b x^2})^{3/2} \, dx\)
3.250
\(\int x^5 (c \sqrt{a+b x^2})^{3/2} \, dx\)
3.251
\(\int x^3 (c \sqrt{a+b x^2})^{3/2} \, dx\)
3.252
\(\int x (c \sqrt{a+b x^2})^{3/2} \, dx\)
3.253
\(\int \frac{(c \sqrt{a+b x^2})^{3/2}}{x} \, dx\)
3.254
\(\int \frac{(c \sqrt{a+b x^2})^{3/2}}{x^3} \, dx\)
3.255
\(\int x^2 (c \sqrt{a+b x^2})^{3/2} \, dx\)
3.256
\(\int (c \sqrt{a+b x^2})^{3/2} \, dx\)
3.257
\(\int \frac{(c \sqrt{a+b x^2})^{3/2}}{x^2} \, dx\)
3.258
\(\int \frac{(c \sqrt{a+b x^2})^{3/2}}{x^4} \, dx\)
3.259
\(\int \sqrt{(b-x) (-a+x)} \, dx\)
3.260
\(\int \sqrt{(1-x^2) (3+x^2)} \, dx\)
3.261
\(\int \frac{1}{\sqrt{(b-x) (-a+x)}} \, dx\)
3.262
\(\int \frac{1}{\sqrt{(1-x^2) (3+x^2)}} \, dx\)
3.263
\(\int x^5 \sqrt{\frac{e (a+b x^2)}{c+d x^2}} \, dx\)
3.264
\(\int x^3 \sqrt{\frac{e (a+b x^2)}{c+d x^2}} \, dx\)
3.265
\(\int x \sqrt{\frac{e (a+b x^2)}{c+d x^2}} \, dx\)
3.266
\(\int \frac{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}}{x} \, dx\)
3.267
\(\int \frac{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}}{x^3} \, dx\)
3.268
\(\int \frac{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}}{x^5} \, dx\)
3.269
\(\int \frac{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}}{x^7} \, dx\)
3.270
\(\int x^4 \sqrt{\frac{e (a+b x^2)}{c+d x^2}} \, dx\)
3.271
\(\int x^2 \sqrt{\frac{e (a+b x^2)}{c+d x^2}} \, dx\)
3.272
\(\int \sqrt{\frac{e (a+b x^2)}{c+d x^2}} \, dx\)
3.273
\(\int \frac{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}}{x^2} \, dx\)
3.274
\(\int \frac{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}}{x^4} \, dx\)
3.275
\(\int \frac{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}}{x^6} \, dx\)
3.276
\(\int x^5 (\frac{e (a+b x^2)}{c+d x^2})^{3/2} \, dx\)
3.277
\(\int x^3 (\frac{e (a+b x^2)}{c+d x^2})^{3/2} \, dx\)
3.278
\(\int x (\frac{e (a+b x^2)}{c+d x^2})^{3/2} \, dx\)
3.279
\(\int \frac{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}}{x} \, dx\)
3.280
\(\int \frac{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}}{x^3} \, dx\)
3.281
\(\int \frac{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}}{x^5} \, dx\)
3.282
\(\int \frac{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}}{x^7} \, dx\)
3.283
\(\int x^4 (\frac{e (a+b x^2)}{c+d x^2})^{3/2} \, dx\)
3.284
\(\int x^2 (\frac{e (a+b x^2)}{c+d x^2})^{3/2} \, dx\)
3.285
\(\int (\frac{e (a+b x^2)}{c+d x^2})^{3/2} \, dx\)
3.286
\(\int \frac{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}}{x^2} \, dx\)
3.287
\(\int \frac{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}}{x^4} \, dx\)
3.288
\(\int \frac{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}}{x^6} \, dx\)
3.289
\(\int x \sqrt{\frac{1-x^2}{1+x^2}} \, dx\)
3.290
\(\int x \sqrt{\frac{5-7 x^2}{7+5 x^2}} \, dx\)
3.291
\(\int x^2 \sqrt{\frac{1-x^3}{1+x^3}} \, dx\)
3.292
\(\int x^8 \sqrt{\frac{1-x^3}{1+x^3}} \, dx\)
3.293
\(\int x^9 \sqrt{\frac{5-7 x^5}{7+5 x^5}} \, dx\)
3.294
\(\int \frac{\sqrt{\frac{x^2}{-1+x^2}}}{1+x^2} \, dx\)
3.295
\(\int \frac{\sqrt{\frac{x^2}{-1+a+(1+a) x^2}}}{1+x^2} \, dx\)
3.296
\(\int \frac{x^5}{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.297
\(\int \frac{x^3}{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.298
\(\int \frac{x}{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.299
\(\int \frac{1}{x \sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.300
\(\int \frac{1}{x^3 \sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.301
\(\int \frac{1}{x^5 \sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.302
\(\int \frac{x^4}{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.303
\(\int \frac{x^2}{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.304
\(\int \frac{1}{\sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.305
\(\int \frac{1}{x^2 \sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.306
\(\int \frac{1}{x^4 \sqrt{\frac{e (a+b x^2)}{c+d x^2}}} \, dx\)
3.307
\(\int \frac{x^5}{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.308
\(\int \frac{x^3}{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.309
\(\int \frac{x}{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.310
\(\int \frac{1}{x (\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.311
\(\int \frac{1}{x^3 (\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.312
\(\int \frac{1}{x^5 (\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.313
\(\int \frac{x^4}{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.314
\(\int \frac{x^2}{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.315
\(\int \frac{1}{(\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.316
\(\int \frac{1}{x^2 (\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.317
\(\int \frac{1}{x^4 (\frac{e (a+b x^2)}{c+d x^2})^{3/2}} \, dx\)
3.318
\(\int x^5 \sqrt{a+\frac{b}{c+d x^2}} \, dx\)
3.319
\(\int x^3 \sqrt{a+\frac{b}{c+d x^2}} \, dx\)
3.320
\(\int x \sqrt{a+\frac{b}{c+d x^2}} \, dx\)
3.321
\(\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x} \, dx\)
3.322
\(\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^3} \, dx\)
3.323
\(\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^5} \, dx\)
3.324
\(\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^7} \, dx\)
3.325
\(\int x^4 \sqrt{a+\frac{b}{c+d x^2}} \, dx\)
3.326
\(\int x^2 \sqrt{a+\frac{b}{c+d x^2}} \, dx\)
3.327
\(\int \sqrt{a+\frac{b}{c+d x^2}} \, dx\)
3.328
\(\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^2} \, dx\)
3.329
\(\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^4} \, dx\)
3.330
\(\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^6} \, dx\)
3.331
\(\int x^5 (a+\frac{b}{c+d x^2})^{3/2} \, dx\)
3.332
\(\int x^3 (a+\frac{b}{c+d x^2})^{3/2} \, dx\)
3.333
\(\int x (a+\frac{b}{c+d x^2})^{3/2} \, dx\)
3.334
\(\int \frac{(a+\frac{b}{c+d x^2})^{3/2}}{x} \, dx\)
3.335
\(\int \frac{(a+\frac{b}{c+d x^2})^{3/2}}{x^3} \, dx\)
3.336
\(\int \frac{(a+\frac{b}{c+d x^2})^{3/2}}{x^5} \, dx\)
3.337
\(\int \frac{(a+\frac{b}{c+d x^2})^{3/2}}{x^7} \, dx\)
3.338
\(\int x^4 (a+\frac{b}{c+d x^2})^{3/2} \, dx\)
3.339
\(\int x^2 (a+\frac{b}{c+d x^2})^{3/2} \, dx\)
3.340
\(\int (a+\frac{b}{c+d x^2})^{3/2} \, dx\)
3.341
\(\int \frac{(a+\frac{b}{c+d x^2})^{3/2}}{x^2} \, dx\)
3.342
\(\int \frac{(a+\frac{b}{c+d x^2})^{3/2}}{x^4} \, dx\)
3.343
\(\int \frac{(a+\frac{b}{c+d x^2})^{3/2}}{x^6} \, dx\)
3.344
\(\int \frac{x^5}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.345
\(\int \frac{x^3}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.346
\(\int \frac{x}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.347
\(\int \frac{1}{x \sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.348
\(\int \frac{1}{x^3 \sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.349
\(\int \frac{1}{x^5 \sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.350
\(\int \frac{x^4}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.351
\(\int \frac{x^2}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.352
\(\int \frac{1}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.353
\(\int \frac{1}{x^2 \sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.354
\(\int \frac{1}{x^4 \sqrt{a+\frac{b}{c+d x^2}}} \, dx\)
3.355
\(\int \frac{x^5}{(a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.356
\(\int \frac{x^3}{(a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.357
\(\int \frac{x}{(a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.358
\(\int \frac{1}{x (a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.359
\(\int \frac{1}{x^3 (a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.360
\(\int \frac{1}{x^5 (a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.361
\(\int \frac{x^4}{(a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.362
\(\int \frac{x^2}{(a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.363
\(\int \frac{1}{(a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.364
\(\int \frac{1}{x^2 (a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.365
\(\int \frac{1}{x^4 (a+\frac{b}{c+d x^2})^{3/2}} \, dx\)
3.366
\(\int \frac{\sqrt{a x^{23}}}{\sqrt{1+x^5}} \, dx\)
3.367
\(\int \frac{\sqrt{a x^{13}}}{\sqrt{1+x^5}} \, dx\)
3.368
\(\int \frac{\sqrt{a x^3}}{\sqrt{1+x^5}} \, dx\)
3.369
\(\int \frac{\sqrt{\frac{a}{x^7}}}{\sqrt{1+x^5}} \, dx\)
3.370
\(\int \frac{\sqrt{\frac{a}{x^{17}}}}{\sqrt{1+x^5}} \, dx\)
3.371
\(\int \frac{\sqrt{a x^6}}{x (1-x^4)} \, dx\)
3.372
\(\int \frac{\sqrt{a x^6}}{x-x^5} \, dx\)
3.373
\(\int \frac{(a x^6)^{3/2}}{x (1-x^4)} \, dx\)
3.374
\(\int (\frac{1}{1-x^4}-\frac{\sqrt{a x^6}}{x (1-x^4)}) \, dx\)
3.375
\(\int (\frac{1}{1-x^4}-\frac{\sqrt{a x^6}}{x-x^5}) \, dx\)
3.376
\(\int \frac{\sqrt{a x^3}}{x-x^3} \, dx\)
3.377
\(\int \frac{\sqrt{a x^4}}{\sqrt{1+x^2}} \, dx\)
3.378
\(\int \frac{\sqrt{a x^3}}{\sqrt{1+x^2}} \, dx\)
3.379
\(\int \frac{\sqrt{a x^2}}{\sqrt{1+x^2}} \, dx\)
3.380
\(\int \frac{\sqrt{a x}}{\sqrt{1+x^2}} \, dx\)
3.381
\(\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{1+x^2}} \, dx\)
3.382
\(\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{1+x^2}} \, dx\)
3.383
\(\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{1+x^2}} \, dx\)
3.384
\(\int \frac{\sqrt{\frac{a}{x^4}}}{\sqrt{1+x^2}} \, dx\)
3.385
\(\int \frac{\sqrt{a x^4}}{\sqrt{1+x^3}} \, dx\)
3.386
\(\int \frac{\sqrt{a x^3}}{\sqrt{1+x^3}} \, dx\)
3.387
\(\int \frac{\sqrt{a x^2}}{\sqrt{1+x^3}} \, dx\)
3.388
\(\int \frac{\sqrt{a x}}{\sqrt{1+x^3}} \, dx\)
3.389
\(\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{1+x^3}} \, dx\)
3.390
\(\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{1+x^3}} \, dx\)
3.391
\(\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{1+x^3}} \, dx\)
3.392
\(\int \frac{\sqrt{\frac{a}{x^4}}}{\sqrt{1+x^3}} \, dx\)
3.393
\(\int \frac{\sqrt{a x^{2 n}}}{\sqrt{1+x^n}} \, dx\)
3.394
\(\int \frac{\sqrt{a x^n}}{\sqrt{1+x^n}} \, dx\)
3.395
\(\int \frac{\sqrt{a x^{n/2}}}{\sqrt{1+x^n}} \, dx\)
3.396
\(\int (\frac{\sqrt{a x^{2 n}}}{\sqrt{1+x^n}}+\frac{2 x^{-n} \sqrt{a x^{2 n}}}{(2+n) \sqrt{1+x^n}}) \, dx\)
3.397
\(\int \frac{\sqrt{a x}}{\sqrt{d+e x} \sqrt{e+f x}} \, dx\)
3.398
\(\int (a x^m)^r \, dx\)
3.399
\(\int (a x^m)^r (b x^n)^s \, dx\)
3.400
\(\int (a x^m)^r (b x^n)^s (c x^p)^t \, dx\)
3.401
\(\int \frac{x^2}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx\)
3.402
\(\int \frac{x}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx\)
3.403
\(\int \frac{1}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx\)
3.404
\(\int \frac{1}{x (\sqrt{a+b x}+\sqrt{c+b x})} \, dx\)
3.405
\(\int \frac{1}{x^2 (\sqrt{a+b x}+\sqrt{c+b x})} \, dx\)
3.406
\(\int \frac{x^2}{(\sqrt{a+b x}+\sqrt{c+b x})^2} \, dx\)
3.407
\(\int \frac{x}{(\sqrt{a+b x}+\sqrt{c+b x})^2} \, dx\)
3.408
\(\int \frac{1}{(\sqrt{a+b x}+\sqrt{c+b x})^2} \, dx\)
3.409
\(\int \frac{1}{x (\sqrt{a+b x}+\sqrt{c+b x})^2} \, dx\)
3.410
\(\int \frac{1}{x^2 (\sqrt{a+b x}+\sqrt{c+b x})^2} \, dx\)
3.411
\(\int \frac{x^2}{(\sqrt{a+b x}+\sqrt{c+b x})^3} \, dx\)
3.412
\(\int \frac{x}{(\sqrt{a+b x}+\sqrt{c+b x})^3} \, dx\)
3.413
\(\int \frac{1}{(\sqrt{a+b x}+\sqrt{c+b x})^3} \, dx\)
3.414
\(\int \frac{1}{x (\sqrt{a+b x}+\sqrt{c+b x})^3} \, dx\)
3.415
\(\int \frac{1}{x^2 (\sqrt{a+b x}+\sqrt{c+b x})^3} \, dx\)
3.416
\(\int \frac{1}{\sqrt{x}+\sqrt{1+x}} \, dx\)
3.417
\(\int \frac{1}{\sqrt{-1+x}+\sqrt{x}} \, dx\)
3.418
\(\int \frac{1}{\sqrt{-1+x}+\sqrt{1+x}} \, dx\)
3.419
\(\int x^3 (\sqrt{1-x}+\sqrt{1+x})^2 \, dx\)
3.420
\(\int x^2 (\sqrt{1-x}+\sqrt{1+x})^2 \, dx\)
3.421
\(\int x (\sqrt{1-x}+\sqrt{1+x})^2 \, dx\)
3.422
\(\int (\sqrt{1-x}+\sqrt{1+x})^2 \, dx\)
3.423
\(\int \frac{(\sqrt{1-x}+\sqrt{1+x})^2}{x} \, dx\)
3.424
\(\int \frac{(\sqrt{1-x}+\sqrt{1+x})^2}{x^2} \, dx\)
3.425
\(\int \frac{(\sqrt{1-x}+\sqrt{1+x})^2}{x^3} \, dx\)
3.426
\(\int \frac{x^3}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
3.427
\(\int \frac{x^2}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
3.428
\(\int \frac{x}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
3.429
\(\int \frac{1}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
3.430
\(\int \frac{1}{x (\sqrt{a+b x}+\sqrt{a+c x})} \, dx\)
3.431
\(\int \frac{1}{x^2 (\sqrt{a+b x}+\sqrt{a+c x})} \, dx\)
3.432
\(\int \frac{x^3}{(\sqrt{a+b x}+\sqrt{a+c x})^2} \, dx\)
3.433
\(\int \frac{x^2}{(\sqrt{a+b x}+\sqrt{a+c x})^2} \, dx\)
3.434
\(\int \frac{x}{(\sqrt{a+b x}+\sqrt{a+c x})^2} \, dx\)
3.435
\(\int \frac{1}{(\sqrt{a+b x}+\sqrt{a+c x})^2} \, dx\)
3.436
\(\int \frac{1}{x (\sqrt{a+b x}+\sqrt{a+c x})^2} \, dx\)
3.437
\(\int \frac{1}{x^2 (\sqrt{a+b x}+\sqrt{a+c x})^2} \, dx\)
3.438
\(\int \frac{x^4}{(\sqrt{a+b x}+\sqrt{a+c x})^3} \, dx\)
3.439
\(\int \frac{x^3}{(\sqrt{a+b x}+\sqrt{a+c x})^3} \, dx\)
3.440
\(\int \frac{x^2}{(\sqrt{a+b x}+\sqrt{a+c x})^3} \, dx\)
3.441
\(\int \frac{x}{(\sqrt{a+b x}+\sqrt{a+c x})^3} \, dx\)
3.442
\(\int \frac{1}{(\sqrt{a+b x}+\sqrt{a+c x})^3} \, dx\)
3.443
\(\int \sqrt{1-x} (\sqrt{1-x}+\sqrt{1+x}) \, dx\)
3.444
\(\int x^3 (-\sqrt{1-x}-\sqrt{1+x}) (\sqrt{1-x}+\sqrt{1+x}) \, dx\)
3.445
\(\int x^2 (-\sqrt{1-x}-\sqrt{1+x}) (\sqrt{1-x}+\sqrt{1+x}) \, dx\)
3.446
\(\int x (-\sqrt{1-x}-\sqrt{1+x}) (\sqrt{1-x}+\sqrt{1+x}) \, dx\)
3.447
\(\int (-\sqrt{1-x}-\sqrt{1+x}) (\sqrt{1-x}+\sqrt{1+x}) \, dx\)
3.448
\(\int \frac{(-\sqrt{1-x}-\sqrt{1+x}) (\sqrt{1-x}+\sqrt{1+x})}{x} \, dx\)
3.449
\(\int \frac{(-\sqrt{1-x}-\sqrt{1+x}) (\sqrt{1-x}+\sqrt{1+x})}{x^2} \, dx\)
3.450
\(\int \frac{(-\sqrt{1-x}-\sqrt{1+x}) (\sqrt{1-x}+\sqrt{1+x})}{x^3} \, dx\)
3.451
\(\int \frac{\sqrt{1-x}+\sqrt{1+x}}{-\sqrt{1-x}+\sqrt{1+x}} \, dx\)
3.452
\(\int \frac{-\sqrt{-1+x}+\sqrt{1+x}}{\sqrt{-1+x}+\sqrt{1+x}} \, dx\)
3.453
\(\int (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}})^n \, dx\)
3.454
\(\int (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}})^3 \, dx\)
3.455
\(\int (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}})^2 \, dx\)
3.456
\(\int (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}) \, dx\)
3.457
\(\int \frac{1}{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}} \, dx\)
3.458
\(\int \frac{1}{(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}})^2} \, dx\)
3.459
\(\int \frac{1}{(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}})^3} \, dx\)
3.460
\(\int (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}})^{5/2} \, dx\)
3.461
\(\int (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}})^{3/2} \, dx\)
3.462
\(\int \sqrt{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}} \, dx\)
3.463
\(\int \frac{1}{\sqrt{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}}} \, dx\)
3.464
\(\int \frac{1}{(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}})^{3/2}} \, dx\)
3.465
\(\int \frac{1}{(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}})^{5/2}} \, dx\)
3.466
\(\int \sqrt{x-\sqrt{-4+x^2}} \, dx\)
3.467
\(\int \sqrt{a x+b \sqrt{c+\frac{a^2 x^2}{b^2}}} \, dx\)
3.468
\(\int \sqrt{1+\sqrt{1-x^2}} \, dx\)
3.469
\(\int \sqrt{1+\sqrt{1+x^2}} \, dx\)
3.470
\(\int \sqrt{5+\sqrt{25+x^2}} \, dx\)
3.471
\(\int \sqrt{a+b \sqrt{\frac{a^2}{b^2}+c x^2}} \, dx\)
3.472
\(\int (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}})^n \, dx\)
3.473
\(\int (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}})^3 \, dx\)
3.474
\(\int (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}})^2 \, dx\)
3.475
\(\int (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}) \, dx\)
3.476
\(\int \frac{1}{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}} \, dx\)
3.477
\(\int \frac{1}{(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}})^2} \, dx\)
3.478
\(\int \frac{1}{(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}})^3} \, dx\)
3.479
\(\int (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}})^{5/2} \, dx\)
3.480
\(\int (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}})^{3/2} \, dx\)
3.481
\(\int \sqrt{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}} \, dx\)
3.482
\(\int \frac{1}{\sqrt{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}}} \, dx\)
3.483
\(\int \frac{1}{(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}})^{3/2}} \, dx\)
3.484
\(\int \frac{1}{(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}})^{5/2}} \, dx\)
3.485
\(\int (a+x^2)^2 (x+\sqrt{a+x^2})^n \, dx\)
3.486
\(\int (a+x^2) (x+\sqrt{a+x^2})^n \, dx\)
3.487
\(\int (x+\sqrt{a+x^2})^n \, dx\)
3.488
\(\int \frac{(x+\sqrt{a+x^2})^n}{a+x^2} \, dx\)
3.489
\(\int \frac{(x+\sqrt{a+x^2})^n}{(a+x^2)^2} \, dx\)
3.490
\(\int (a+x^2)^2 (x-\sqrt{a+x^2})^n \, dx\)
3.491
\(\int (a+x^2) (x-\sqrt{a+x^2})^n \, dx\)
3.492
\(\int (x-\sqrt{a+x^2})^n \, dx\)
3.493
\(\int \frac{(x-\sqrt{a+x^2})^n}{a+x^2} \, dx\)
3.494
\(\int \frac{(x-\sqrt{a+x^2})^n}{(a+x^2)^2} \, dx\)
3.495
\(\int (a+x^2)^{5/2} (x+\sqrt{a+x^2})^n \, dx\)
3.496
\(\int (a+x^2)^{3/2} (x+\sqrt{a+x^2})^n \, dx\)
3.497
\(\int \sqrt{a+x^2} (x+\sqrt{a+x^2})^n \, dx\)
3.498
\(\int \frac{(x+\sqrt{a+x^2})^n}{\sqrt{a+x^2}} \, dx\)
3.499
\(\int \frac{(x+\sqrt{a+x^2})^n}{(a+x^2)^{3/2}} \, dx\)
3.500
\(\int \frac{(x+\sqrt{a+x^2})^n}{(a+x^2)^{5/2}} \, dx\)
3.501
\(\int (a+x^2)^{5/2} (x-\sqrt{a+x^2})^n \, dx\)
3.502
\(\int (a+x^2)^{3/2} (x-\sqrt{a+x^2})^n \, dx\)
3.503
\(\int \sqrt{a+x^2} (x-\sqrt{a+x^2})^n \, dx\)
3.504
\(\int \frac{(x-\sqrt{a+x^2})^n}{\sqrt{a+x^2}} \, dx\)
3.505
\(\int \frac{(x-\sqrt{a+x^2})^n}{(a+x^2)^{3/2}} \, dx\)
3.506
\(\int \frac{(x-\sqrt{a+x^2})^n}{(a+x^2)^{5/2}} \, dx\)
3.507
\(\int (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2})^2 (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n \, dx\)
3.508
\(\int (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}) (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n \, dx\)
3.509
\(\int (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n \, dx\)
3.510
\(\int \frac{(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n}{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \, dx\)
3.511
\(\int \frac{(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n}{(a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2})^2} \, dx\)
3.512
\(\int (d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}})^n \, dx\)
3.513
\(\int \frac{(d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}})^n}{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \, dx\)
3.514
\(\int (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2})^{3/2} (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n \, dx\)
3.515
\(\int \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n \, dx\)
3.516
\(\int \frac{(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n}{\sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}} \, dx\)
3.517
\(\int \frac{(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n}{(a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2})^{3/2}} \, dx\)
3.518
\(\int \frac{(d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}})^n}{\sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}} \, dx\)
3.519
\(\int \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n \, dx\)
3.520
\(\int \frac{(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n}{\sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}} \, dx\)
3.521
\(\int \frac{(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}})^n}{(a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2})^{3/2}} \, dx\)
3.522
\(\int \frac{(d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}})^n}{\sqrt{\frac{a f^2 g+e g x (2 d+e x)}{f^2}}} \, dx\)
3.523
\(\int \frac{1}{(a+b x) \sqrt{c+d x^2} \sqrt{e+f x^2}} \, dx\)
3.524
\(\int \frac{e-2 f x^2}{e^2+4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\)
3.525
\(\int \frac{e-2 f x^2}{e^2-4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\)
3.526
\(\int \frac{e-4 f x^3}{e^2+4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\)
3.527
\(\int \frac{e-4 f x^3}{e^2-4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\)
3.528
\(\int \frac{e-2 f (-1+n) x^n}{e^2+4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
3.529
\(\int \frac{e-2 f (-1+n) x^n}{e^2-4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
3.530
\(\int \frac{x}{e^2+4 e f x^2+4 d f x^4+4 f^2 x^4} \, dx\)
3.531
\(\int \frac{x}{e^2+4 e f x^2-4 d f x^4+4 f^2 x^4} \, dx\)
3.532
\(\int \frac{x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^6} \, dx\)
3.533
\(\int \frac{x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^6} \, dx\)
3.534
\(\int \frac{x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^{2+2 m}} \, dx\)
3.535
\(\int \frac{x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^{2+2 m}} \, dx\)
3.536
\(\int \frac{x (2 e-2 f x^3)}{e^2+4 e f x^3+4 d f x^4+4 f^2 x^6} \, dx\)
3.537
\(\int \frac{x (2 e-2 f x^3)}{e^2+4 e f x^3-4 d f x^4+4 f^2 x^6} \, dx\)
3.538
\(\int \frac{x^2}{e^2+4 e f x^3+4 d f x^6+4 f^2 x^6} \, dx\)
3.539
\(\int \frac{x^2}{e^2+4 e f x^3-4 d f x^6+4 f^2 x^6} \, dx\)
3.540
\(\int \frac{x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6+4 d f x^{2+2 m}} \, dx\)
3.541
\(\int \frac{x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6-4 d f x^{2+2 m}} \, dx\)
3.542
\(\int \frac{x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2+4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
3.543
\(\int \frac{x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2-4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
3.544
\(\int \frac{x^5}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.545
\(\int \frac{x^3}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.546
\(\int \frac{x}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.547
\(\int \frac{1}{x (a c+b c x^2+d \sqrt{a+b x^2})} \, dx\)
3.548
\(\int \frac{1}{x^3 (a c+b c x^2+d \sqrt{a+b x^2})} \, dx\)
3.549
\(\int \frac{x^2}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.550
\(\int \frac{1}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
3.551
\(\int \frac{1}{x^2 (a c+b c x^2+d \sqrt{a+b x^2})} \, dx\)
3.552
\(\int \frac{x^8}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.553
\(\int \frac{x^5}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.554
\(\int \frac{x^2}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.555
\(\int \frac{1}{x (a c+b c x^3+d \sqrt{a+b x^3})} \, dx\)
3.556
\(\int \frac{1}{x^4 (a c+b c x^3+d \sqrt{a+b x^3})} \, dx\)
3.557
\(\int \frac{x^3}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.558
\(\int \frac{x}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.559
\(\int \frac{1}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
3.560
\(\int \frac{1}{x^2 (a c+b c x^3+d \sqrt{a+b x^3})} \, dx\)
3.561
\(\int \frac{1}{x^3 (a c+b c x^3+d \sqrt{a+b x^3})} \, dx\)
3.562
\(\int \frac{1}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx\)
3.563
\(\int \frac{x^m}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx\)
3.564
\(\int \frac{x^{-1+n}}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx\)
3.565
\(\int \frac{1}{\sqrt{x}+4 x^{3/2}} \, dx\)
3.566
\(\int \frac{1}{\sqrt{x}-x^{5/2}} \, dx\)
3.567
\(\int \frac{1}{-\sqrt [4]{x}+\sqrt{x}} \, dx\)
3.568
\(\int \frac{1}{\sqrt [3]{x}+\sqrt{x}} \, dx\)
3.569
\(\int \frac{1}{\sqrt [4]{x}+\sqrt{x}} \, dx\)
3.570
\(\int \frac{1}{-\sqrt [3]{x}+x^{2/3}} \, dx\)
3.571
\(\int \frac{1}{\frac{1}{\sqrt [4]{x}}+\sqrt{x}} \, dx\)
3.572
\(\int \frac{1}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\)
3.573
\(\int \frac{1}{\frac{1}{\sqrt [3]{x}}+\frac{1}{\sqrt [4]{x}}} \, dx\)
3.574
\(\int \frac{1}{-\frac{1}{\sqrt [3]{x}}+\sqrt{x}} \, dx\)
3.575
\(\int \frac{\sqrt{x}}{x+x^2} \, dx\)
3.576
\(\int \frac{x}{4 \sqrt{x}+x} \, dx\)
3.577
\(\int \frac{\sqrt{x}}{\sqrt [3]{x}+x} \, dx\)
3.578
\(\int \frac{\sqrt [3]{x}}{\sqrt [4]{x}+\sqrt{x}} \, dx\)
3.579
\(\int \frac{\sqrt{x}}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\)
3.580
\(\int \frac{\sqrt{x}}{-\frac{1}{\sqrt [3]{x}}+\sqrt{x}} \, dx\)
3.581
\(\int \frac{\sqrt{b-\frac{a}{x}} x^m}{\sqrt{a-b x}} \, dx\)
3.582
\(\int \frac{\sqrt{b-\frac{a}{x}} x^2}{\sqrt{a-b x}} \, dx\)
3.583
\(\int \frac{\sqrt{b-\frac{a}{x}} x}{\sqrt{a-b x}} \, dx\)
3.584
\(\int \frac{\sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \, dx\)
3.585
\(\int \frac{\sqrt{b-\frac{a}{x}}}{x \sqrt{a-b x}} \, dx\)
3.586
\(\int \frac{\sqrt{b-\frac{a}{x}}}{x^2 \sqrt{a-b x}} \, dx\)
3.587
\(\int (a+\frac{b}{x})^m (c+d x)^n \, dx\)
3.588
\(\int (a+\frac{b}{x})^m (c+d x)^2 \, dx\)
3.589
\(\int (a+\frac{b}{x})^m (c+d x) \, dx\)
3.590
\(\int (a+\frac{b}{x})^m \, dx\)
3.591
\(\int \frac{(a+\frac{b}{x})^m}{c+d x} \, dx\)
3.592
\(\int \frac{(a+\frac{b}{x})^m}{(c+d x)^2} \, dx\)
3.593
\(\int \frac{(a+\frac{b}{x})^m}{(c+d x)^3} \, dx\)
3.594
\(\int \frac{(a+\frac{b}{x})^m}{(c+d x)^4} \, dx\)
3.595
\(\int \frac{\sqrt{b-\frac{a}{x^2}} x^m}{\sqrt{a-b x^2}} \, dx\)
3.596
\(\int \frac{\sqrt{b-\frac{a}{x^2}} x^2}{\sqrt{a-b x^2}} \, dx\)
3.597
\(\int \frac{\sqrt{b-\frac{a}{x^2}} x}{\sqrt{a-b x^2}} \, dx\)
3.598
\(\int \frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \, dx\)
3.599
\(\int \frac{\sqrt{b-\frac{a}{x^2}}}{x \sqrt{a-b x^2}} \, dx\)
3.600
\(\int \frac{\sqrt{b-\frac{a}{x^2}}}{x^2 \sqrt{a-b x^2}} \, dx\)
3.601
\(\int \frac{(c+d x)^{3/2}}{\sqrt{a+\frac{b}{x^2}}} \, dx\)
3.602
\(\int \frac{-1+x^3}{(-4 x+x^4)^{2/3}} \, dx\)
3.603
\(\int (2-x^2) \sqrt [4]{6 x-x^3} \, dx\)
3.604
\(\int (1+x^4) \sqrt{5 x+x^5} \, dx\)
3.605
\(\int (2+5 x^4) \sqrt{2 x+x^5} \, dx\)
3.606
\(\int \frac{x+3 x^2}{\sqrt{x^2+2 x^3}} \, dx\)
3.607
\(\int \frac{2+\sqrt [3]{1-5 x}}{3+\sqrt [3]{1-5 x}} \, dx\)
3.608
\(\int \frac{1+\sqrt{x}}{-1+\sqrt{x}} \, dx\)
3.609
\(\int \frac{1-\sqrt{2+3 x}}{1+\sqrt{2+3 x}} \, dx\)
3.610
\(\int \frac{-1+\sqrt{a+b x}}{1+\sqrt{a+b x}} \, dx\)
3.611
\(\int \frac{a+b n x^{-1+n}}{a x+b x^n} \, dx\)
3.612
\(\int \frac{x^{-n} (a+b n x^{-1+n})}{b+a x^{1-n}} \, dx\)
3.613
\(\int x (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (2 a d+(3 b d+3 a e+b d m+a e n) x+(4 c d+4 b e+4 a f+2 c d m+b e m+b e n+2 a f n) x^2+(5 c e+5 b f+5 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(6 c f+6 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (7+2 m+3 n) x^5) \, dx\)
3.614
\(\int (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (a d+(2 b d+2 a e+b d m+a e n) x+(3 c d+3 b e+3 a f+2 c d m+b e m+b e n+2 a f n) x^2+(4 c e+4 b f+4 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(5 c f+5 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (6+2 m+3 n) x^5) \, dx\)
3.615
\(\int (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (b d+a e+b d m+a e n+(2 c d+2 b e+2 a f+2 c d m+b e m+b e n+2 a f n) x+(3 c e+3 b f+3 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^2+(4 c f+4 b g+2 c f m+b g m+2 c f n+3 b g n) x^3+c g (5+2 m+3 n) x^4) \, dx\)
3.616
\(\int \frac{(a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (-a d+(b d m+a e n) x+(c d+b e+a f+2 c d m+b e m+b e n+2 a f n) x^2+(2 c e+2 b f+2 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(3 c f+3 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (4+2 m+3 n) x^5)}{x^2} \, dx\)
3.617
\(\int \frac{(a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (-2 a d+(-b d-a e+b d m+a e n) x+(2 c d m+b e m+b e n+2 a f n) x^2+(c e+b f+a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(2 c f+2 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (3+2 m+3 n) x^5)}{x^3} \, dx\)
3.618
\(\int x^3 (a+b \sqrt{c+d x})^2 \, dx\)
3.619
\(\int x^2 (a+b \sqrt{c+d x})^2 \, dx\)
3.620
\(\int x (a+b \sqrt{c+d x})^2 \, dx\)
3.621
\(\int (a+b \sqrt{c+d x})^2 \, dx\)
3.622
\(\int \frac{(a+b \sqrt{c+d x})^2}{x} \, dx\)
3.623
\(\int \frac{(a+b \sqrt{c+d x})^2}{x^2} \, dx\)
3.624
\(\int \frac{(a+b \sqrt{c+d x})^2}{x^3} \, dx\)
3.625
\(\int x^3 \sqrt{a+b \sqrt{c+d x}} \, dx\)
3.626
\(\int x^2 \sqrt{a+b \sqrt{c+d x}} \, dx\)
3.627
\(\int x \sqrt{a+b \sqrt{c+d x}} \, dx\)
3.628
\(\int \sqrt{a+b \sqrt{c+d x}} \, dx\)
3.629
\(\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x} \, dx\)
3.630
\(\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x^2} \, dx\)
3.631
\(\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x^3} \, dx\)
3.632
\(\int \frac{x^3}{a+b \sqrt{c+d x}} \, dx\)
3.633
\(\int \frac{x^2}{a+b \sqrt{c+d x}} \, dx\)
3.634
\(\int \frac{x}{a+b \sqrt{c+d x}} \, dx\)
3.635
\(\int \frac{1}{a+b \sqrt{c+d x}} \, dx\)
3.636
\(\int \frac{1}{x (a+b \sqrt{c+d x})} \, dx\)
3.637
\(\int \frac{1}{x^2 (a+b \sqrt{c+d x})} \, dx\)
3.638
\(\int \frac{1}{x^3 (a+b \sqrt{c+d x})} \, dx\)
3.639
\(\int \frac{x^3}{(a+b \sqrt{c+d x})^2} \, dx\)
3.640
\(\int \frac{x^2}{(a+b \sqrt{c+d x})^2} \, dx\)
3.641
\(\int \frac{x}{(a+b \sqrt{c+d x})^2} \, dx\)
3.642
\(\int \frac{1}{(a+b \sqrt{c+d x})^2} \, dx\)
3.643
\(\int \frac{1}{x (a+b \sqrt{c+d x})^2} \, dx\)
3.644
\(\int \frac{1}{x^2 (a+b \sqrt{c+d x})^2} \, dx\)
3.645
\(\int \frac{1}{x^3 (a+b \sqrt{c+d x})^2} \, dx\)
3.646
\(\int \frac{x^3}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.647
\(\int \frac{x^2}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.648
\(\int \frac{x}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.649
\(\int \frac{1}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.650
\(\int \frac{1}{x \sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.651
\(\int \frac{1}{x^2 \sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.652
\(\int \frac{1}{x^3 \sqrt{a+b \sqrt{c+d x}}} \, dx\)
3.653
\(\int x^3 (a+b \sqrt{c+d x})^p \, dx\)
3.654
\(\int x^2 (a+b \sqrt{c+d x})^p \, dx\)
3.655
\(\int x (a+b \sqrt{c+d x})^p \, dx\)
3.656
\(\int (a+b \sqrt{c+d x})^p \, dx\)
3.657
\(\int \frac{(a+b \sqrt{c+d x})^p}{x} \, dx\)
3.658
\(\int \frac{(a+b (c x)^n)^{5/2}}{x} \, dx\)
3.659
\(\int \frac{(a+b (c x)^n)^{3/2}}{x} \, dx\)
3.660
\(\int \frac{\sqrt{a+b (c x)^n}}{x} \, dx\)
3.661
\(\int \frac{1}{x \sqrt{a+b (c x)^n}} \, dx\)
3.662
\(\int \frac{1}{x (a+b (c x)^n)^{3/2}} \, dx\)
3.663
\(\int \frac{1}{x (a+b (c x)^n)^{5/2}} \, dx\)
3.664
\(\int \frac{(-a+b (c x)^n)^{5/2}}{x} \, dx\)
3.665
\(\int \frac{(-a+b (c x)^n)^{3/2}}{x} \, dx\)
3.666
\(\int \frac{\sqrt{-a+b (c x)^n}}{x} \, dx\)
3.667
\(\int \frac{1}{x \sqrt{-a+b (c x)^n}} \, dx\)
3.668
\(\int \frac{1}{x (-a+b (c x)^n)^{3/2}} \, dx\)
3.669
\(\int \frac{1}{x (-a+b (c x)^n)^{5/2}} \, dx\)
3.670
\(\int \frac{1}{x \sqrt{a+b x}} \, dx\)
3.671
\(\int \frac{1}{x \sqrt{a+b (c x)^m}} \, dx\)
3.672
\(\int \frac{1}{x \sqrt{a+b (c (d x)^m)^n}} \, dx\)
3.673
\(\int \frac{1}{x \sqrt{a+b (c (d (e x)^m)^n)^p}} \, dx\)
3.674
\(\int \frac{1}{x \sqrt{a+b (c (d (e (f x)^m)^n)^p)^q}} \, dx\)
3.675
\(\int \frac{\sqrt{-1+\frac{1}{x^2}} (-1+x^2)^3}{x} \, dx\)
3.676
\(\int \frac{\sqrt{-1+\frac{1}{x^2}} (-1+x^2)^2}{x} \, dx\)
3.677
\(\int \frac{\sqrt{-1+\frac{1}{x^2}} (-1+x^2)}{x} \, dx\)
3.678
\(\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x (-1+x^2)} \, dx\)
3.679
\(\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x (-1+x^2)^2} \, dx\)
3.680
\(\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x (-1+x^2)^3} \, dx\)
3.681
\(\int \frac{\sqrt{1+\frac{1}{x^2}} x}{(1+x^2)^2} \, dx\)
3.682
\(\int \frac{1}{\sqrt{1+\frac{1}{x^2}} x (1+x^2)} \, dx\)
3.683
\(\int \frac{x}{a+b x^2+\sqrt{a+b x^2}} \, dx\)
3.684
\(\int \frac{x}{x^2-\sqrt [3]{x^2}} \, dx\)
3.685
\(\int x (1+x^2)^3 \sqrt{2+2 x^2+x^4} \, dx\)
3.686
\(\int x^5 \sqrt{1-x^3} (1+x^9)^2 \, dx\)
3.687
\(\int (\frac{x}{(a+b x^2)^{3/2}}+\frac{x}{(1+x^2) \sqrt{a+b x^2}}) \, dx\)
3.688
\(\int \frac{x (1+a+x^2+b x^2)}{(1+x^2) (a+b x^2)^{3/2}} \, dx\)
3.689
\(\int (\frac{x}{(a+b x^2)^{5/2}}+\frac{x}{(a+b x^2)^{3/2}}+\frac{x}{(1+x^2) \sqrt{a+b x^2}}) \, dx\)
3.690
\(\int \frac{x (1+a+a^2+x^2+a x^2+b x^2+2 a b x^2+b x^4+b^2 x^4)}{(1+x^2) (a+b x^2)^{5/2}} \, dx\)
3.691
\(\int \frac{1}{\sqrt{\sqrt{x}+x}} \, dx\)
3.692
\(\int \sqrt{\sqrt{x}+x} \, dx\)
3.693
\(\int \sqrt{-x} (\sqrt{-x}+x) \, dx\)
3.694
\(\int \frac{5+\sqrt [4]{x}}{-6+x} \, dx\)
3.695
\(\int \frac{1}{4+\sqrt{4-x}-x} \, dx\)
3.696
\(\int \frac{1}{1+x-\sqrt{2+x}} \, dx\)
3.697
\(\int \frac{1}{4+x+\sqrt{1+x}} \, dx\)
3.698
\(\int \frac{1}{x-\sqrt{1+x}} \, dx\)
3.699
\(\int \frac{1}{x-\sqrt{2+x}} \, dx\)
3.700
\(\int \frac{1}{-\sqrt{1-x}+x} \, dx\)
3.701
\(\int \sqrt{1+\sqrt{x}+x} \, dx\)
3.702
\(\int \sqrt{1+x+\sqrt{1+x}} \, dx\)
3.703
\(\int \sqrt{\sqrt{-1+x}+x} \, dx\)
3.704
\(\int \sqrt{2 x+\sqrt{-1+2 x}} \, dx\)
3.705
\(\int \sqrt{3 x+\sqrt{-7+8 x}} \, dx\)
3.706
\(\int \frac{1}{\sqrt{x+\sqrt{1+x}}} \, dx\)
3.707
\(\int \frac{1+x}{4+x+\sqrt{-9+6 x}} \, dx\)
3.708
\(\int \frac{12-x}{4+x+\sqrt{-9+6 x}} \, dx\)
3.709
\(\int \frac{-1+x^3}{\sqrt{x} (1+x^2)} \, dx\)
3.710
\(\int \frac{1}{2 \sqrt{-1+x} \sqrt{-\sqrt{-1+x}+x}} \, dx\)
3.711
\(\int \frac{1+x^{7/2}}{1-x^2} \, dx\)
3.712
\(\int \frac{4+2 x}{\sqrt [3]{-1+2 x}+\sqrt{-1+2 x}} \, dx\)
3.713
\(\int \frac{1}{\sqrt{2+\sqrt{1+\sqrt{x}}}} \, dx\)
3.714
\(\int \sqrt{2+\sqrt{4+\sqrt{x}}} \, dx\)
3.715
\(\int \sqrt{2-\sqrt{4+\sqrt{-9+5 x}}} \, dx\)
3.716
\(\int \frac{1}{\sqrt{2+\sqrt{1+\sqrt{x}}}} \, dx\)
3.717
\(\int \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{x}}}} \, dx\)
3.718
\(\int \sqrt{2+\sqrt{3+\sqrt{-1+2 \sqrt{x}}}} \, dx\)
3.719
\(\int \sqrt{1+\sqrt{1+\sqrt{-1+x}}} x \, dx\)
3.720
\(\int \frac{1}{\sqrt{-1+x} \sqrt{-\sqrt{-1+x}+x}} \, dx\)
3.721
\(\int \frac{1}{\sqrt{1+x+\sqrt{-1+2 x}}} \, dx\)
3.722
\(\int \frac{q+p x}{\sqrt{b+a x} (f+\sqrt{b+a x})} \, dx\)
3.723
\(\int \sqrt{1-\sqrt{x}-x} \, dx\)
3.724
\(\int \frac{9+6 \sqrt{x}+x}{4 \sqrt{x}+x} \, dx\)
3.725
\(\int \frac{6-8 x^{7/2}}{5-9 \sqrt{x}} \, dx\)
3.726
\(\int \frac{\sqrt{1+x} (1+x^3)}{1+x^2} \, dx\)
3.727
\(\int \frac{\sqrt{-1-\sqrt{x}+x}}{(-1+x) \sqrt{x}} \, dx\)
3.728
\(\int \frac{1+2 \sqrt{1+x}}{x \sqrt{1+x} \sqrt{x+\sqrt{1+x}}} \, dx\)
3.729
\(\int \frac{1}{\sqrt{x} \sqrt{1+x}} \, dx\)
3.730
\(\int \frac{\sqrt{\frac{x}{1+x}}}{x} \, dx\)
3.731
\(\int \frac{\sqrt{x}}{\sqrt{1+x}} \, dx\)
3.732
\(\int \sqrt{\frac{x}{1+x}} \, dx\)
3.733
\(\int \frac{\sqrt{-1+x}}{x^2 \sqrt{1+x}} \, dx\)
3.734
\(\int \frac{\sqrt{\frac{-1+x}{1+x}}}{x^2} \, dx\)
3.735
\(\int \frac{\sqrt{-1+x} x^3}{\sqrt{1+x}} \, dx\)
3.736
\(\int x^3 \sqrt{\frac{-1+x}{1+x}} \, dx\)
3.737
\(\int \frac{\sqrt{-\frac{x}{1+x}}}{x} \, dx\)
3.738
\(\int \frac{\sqrt{\frac{1-x}{1+x}}}{-1+x} \, dx\)
3.739
\(\int \frac{\sqrt{\frac{a+b x}{c-b x}}}{a+b x} \, dx\)
3.740
\(\int \frac{\sqrt{\frac{a+b x}{c+d x}}}{a+b x} \, dx\)
3.741
\(\int \sqrt{-\frac{x}{1+x}} \, dx\)
3.742
\(\int \sqrt{\frac{1-x}{1+x}} \, dx\)
3.743
\(\int \sqrt{\frac{a+x}{a-x}} \, dx\)
3.744
\(\int \sqrt{\frac{-a+x}{a+x}} \, dx\)
3.745
\(\int \sqrt{\frac{a+b x}{c+d x}} \, dx\)
3.746
\(\int \sqrt{\frac{-1+x}{5+3 x}} \, dx\)
3.747
\(\int \frac{\sqrt{\frac{-1+5 x}{1+7 x}}}{x^2} \, dx\)
3.748
\(\int \frac{x}{\sqrt{\frac{1-x}{1+x}} (1+x)} \, dx\)
3.749
\(\int \frac{x}{(1+x) \sqrt{-1+\frac{2}{1+x}}} \, dx\)
3.750
\(\int \frac{x}{(1+x) \sqrt{\frac{2+x}{3+x}}} \, dx\)
3.751
\(\int \frac{\sqrt{1+\frac{1}{x}}}{(1+x)^2} \, dx\)
3.752
\(\int \frac{\sqrt{1+\frac{1}{x}}}{\sqrt{1-x^2}} \, dx\)
3.753
\(\int \frac{1}{x+\sqrt{3-2 x-x^2}} \, dx\)
3.754
\(\int \frac{1}{(x+\sqrt{3-2 x-x^2})^2} \, dx\)
3.755
\(\int \frac{1}{(x+\sqrt{3-2 x-x^2})^3} \, dx\)
3.756
\(\int \frac{1}{x+\sqrt{-3-2 x+x^2}} \, dx\)
3.757
\(\int \frac{1}{(x+\sqrt{-3-2 x+x^2})^2} \, dx\)
3.758
\(\int \frac{1}{(x+\sqrt{-3-2 x+x^2})^3} \, dx\)
3.759
\(\int \frac{1}{x+\sqrt{-3-4 x-x^2}} \, dx\)
3.760
\(\int \frac{1}{(x+\sqrt{-3-4 x-x^2})^2} \, dx\)
3.761
\(\int \frac{1}{(x+\sqrt{-3-4 x-x^2})^3} \, dx\)
3.762
\(\int x^3 (1+x)^3 (1+2 x) \sqrt{1-x^2-2 x^3-x^4} \, dx\)
3.763
\(\int (1+2 x) (x+x^2)^3 \sqrt{1-(x+x^2)^2} \, dx\)
3.764
\(\int (8 x-8 x^2+4 x^3-x^4)^{3/2} \, dx\)
3.765
\(\int \sqrt{8 x-8 x^2+4 x^3-x^4} \, dx\)
3.766
\(\int \frac{1}{\sqrt{8 x-8 x^2+4 x^3-x^4}} \, dx\)
3.767
\(\int \frac{1}{(8 x-8 x^2+4 x^3-x^4)^{3/2}} \, dx\)
3.768
\(\int \frac{1}{(8 x-8 x^2+4 x^3-x^4)^{5/2}} \, dx\)
3.769
\(\int ((2-x) x (4-2 x+x^2))^{3/2} \, dx\)
3.770
\(\int \sqrt{(2-x) x (4-2 x+x^2)} \, dx\)
3.771
\(\int \frac{1}{\sqrt{(2-x) x (4-2 x+x^2)}} \, dx\)
3.772
\(\int \frac{1}{((2-x) x (4-2 x+x^2))^{3/2}} \, dx\)
3.773
\(\int \frac{1}{((2-x) x (4-2 x+x^2))^{5/2}} \, dx\)
3.774
\(\int (4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4)^{3/2} \, dx\)
3.775
\(\int \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4} \, dx\)
3.776
\(\int \frac{1}{\sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}} \, dx\)
3.777
\(\int \frac{1}{(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4)^{3/2}} \, dx\)
3.778
\(\int \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4} \, dx\)
3.779
\(\int \frac{1}{\sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}} \, dx\)
3.780
\(\int \frac{1}{(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4)^{3/2}} \, dx\)
3.781
\(\int (a+8 x-8 x^2+4 x^3-x^4)^{3/2} \, dx\)
3.782
\(\int \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx\)
3.783
\(\int \frac{1}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx\)
3.784
\(\int \frac{1}{(a+8 x-8 x^2+4 x^3-x^4)^{3/2}} \, dx\)
3.785
\(\int \frac{1}{(a+8 x-8 x^2+4 x^3-x^4)^{5/2}} \, dx\)
3.786
\(\int x (a+8 x-8 x^2+4 x^3-x^4)^{3/2} \, dx\)
3.787
\(\int x \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx\)
3.788
\(\int \frac{x}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx\)
3.789
\(\int \frac{x}{(a+8 x-8 x^2+4 x^3-x^4)^{3/2}} \, dx\)
3.790
\(\int \frac{x}{(a+8 x-8 x^2+4 x^3-x^4)^{5/2}} \, dx\)
3.791
\(\int x^2 (a+8 x-8 x^2+4 x^3-x^4)^{3/2} \, dx\)
3.792
\(\int x^2 \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx\)
3.793
\(\int \frac{x^2}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx\)
3.794
\(\int \frac{x^2}{(a+8 x-8 x^2+4 x^3-x^4)^{3/2}} \, dx\)
3.795
\(\int \frac{x^2}{(a+8 x-8 x^2+4 x^3-x^4)^{5/2}} \, dx\)
3.796
\(\int \frac{1}{\sqrt{8+8 x-x^3+8 x^4}} \, dx\)
3.797
\(\int \frac{1}{(8+8 x-x^3+8 x^4)^{3/2}} \, dx\)
3.798
\(\int \frac{1}{\sqrt{1+4 x+4 x^2+4 x^4}} \, dx\)
3.799
\(\int \frac{1}{(1+4 x+4 x^2+4 x^4)^{3/2}} \, dx\)
3.800
\(\int \frac{1}{\sqrt{8+24 x+8 x^2-15 x^3+8 x^4}} \, dx\)
3.801
\(\int \frac{1}{(8+24 x+8 x^2-15 x^3+8 x^4)^{3/2}} \, dx\)
3.802
\(\int \frac{1}{(8+24 x+8 x^2-15 x^3+8 x^4)^{5/2}} \, dx\)
3.803
\(\int \frac{1}{\sqrt{9-6 x-44 x^2+15 x^3+3 x^4}} \, dx\)
3.804
\(\int \frac{1}{(9-6 x-44 x^2+15 x^3+3 x^4)^{3/2}} \, dx\)
3.805
\(\int \frac{(2 \sqrt{3-x}+\frac{3}{\sqrt{1+x}})^2}{x} \, dx\)
3.806
\(\int \frac{-1+x+x^2}{1+\sqrt{1+x^2}} \, dx\)
3.807
\(\int \frac{-1+x+x^2}{1+x+\sqrt{1+x^2}} \, dx\)
3.808
\(\int \frac{2 \sqrt{-1+x}+x}{\sqrt{-1+x} x} \, dx\)
3.809
\(\int (a+c \sqrt{x}+b x^{2/3})^2 \, dx\)
3.810
\(\int (a+c \sqrt{x}+b x^{2/3})^3 \, dx\)
3.811
\(\int \frac{-1+x^2}{\sqrt{a-b+\frac{b}{x^2}} x^3} \, dx\)
3.812
\(\int \frac{-1+x^2}{\sqrt{a+b (-1+\frac{1}{x^2})} x^3} \, dx\)
3.813
\(\int \frac{1+x}{(4+x^2) \sqrt{9+x^2}} \, dx\)
3.814
\(\int x (1+\sqrt{1-x^2}) \, dx\)
3.815
\(\int x (1+\sqrt{1-x} \sqrt{1+x}) \, dx\)
3.816
\(\int x (1+\frac{1}{\sqrt{2+x} \sqrt{3+x}}) \, dx\)
3.817
\(\int \frac{x-\sqrt{x^6}}{x (1-x^4)} \, dx\)
3.818
\(\int \frac{1-\frac{\sqrt{x^6}}{x}}{1-x^4} \, dx\)
3.819
\(\int \frac{x-\sqrt{x^6}}{x-x^5} \, dx\)
3.820
\(\int \frac{x}{x+\sqrt{x^6}} \, dx\)
3.821
\(\int \frac{\sqrt{x}-\sqrt{x^3}}{x-x^3} \, dx\)
3.822
\(\int \frac{1}{\sqrt{x}+\sqrt{x^3}} \, dx\)
3.823
\(\int \frac{1}{\sqrt{-1+x}+\sqrt{(-1+x)^3}} \, dx\)
3.824
\(\int (-\frac{3}{(4+5 x)^2}-\frac{5+4 x}{(4+5 x)^2 \sqrt{1-x^2}}) \, dx\)
3.825
\(\int \frac{-5-4 x-3 \sqrt{1-x^2}}{(4+5 x)^2 \sqrt{1-x^2}} \, dx\)
3.826
\(\int \frac{1}{(-5-4 x) \sqrt{1-x^2}+3 (1-x^2)} \, dx\)
3.827
\(\int \frac{1}{3-3 x^2-5 \sqrt{1-x^2}-4 x \sqrt{1-x^2}} \, dx\)
3.828
\(\int \frac{-1+\sqrt{1-x^2}}{\sqrt{1-x^2} (2+x-2 \sqrt{1-x^2})^2} \, dx\)
3.829
\(\int \frac{a+b x^{-1+n}}{c x+d x^n} \, dx\)
3.830
\(\int \frac{\sqrt{1+2 x^2}}{1+\sqrt{1+2 x^2}} \, dx\)
3.831
\(\int \frac{\sqrt{-1+4 x^2}}{x+\sqrt{-1+4 x^2}} \, dx\)
3.832
\(\int \frac{a+b x+c x^2}{(d+e x)^3 \sqrt{-1+x^2}} \, dx\)
3.833
\(\int \frac{1+2 x^8}{x (1+x^8)^{3/2}} \, dx\)
3.834
\(\int \frac{\sqrt{1+x^8} (1+2 x^8)}{x+2 x^9+x^{17}} \, dx\)
3.835
\(\int (1-9 x^2+\frac{x}{\sqrt{1-9 x^2}}) \, dx\)
3.836
\(\int \frac{x+(1-9 x^2)^{3/2}}{\sqrt{1-9 x^2}} \, dx\)
3.837
\(\int \frac{(-3+2 \sqrt{x}) (-3 \sqrt{x}+x)^{2/3}}{\sqrt{x}} \, dx\)
3.838
\(\int \frac{9-9 \sqrt{x}+2 x}{\sqrt [3]{-3 \sqrt{x}+x}} \, dx\)
3.839
\(\int \frac{1}{\sqrt{4-9 x^2}} \, dx\)
3.840
\(\int \frac{1}{\sqrt{2-3 x} \sqrt{2+3 x}} \, dx\)
3.841
\(\int \frac{1}{\sqrt{(2-3 x) (2+3 x)}} \, dx\)
3.842
\(\int \frac{1}{\sqrt{15-2 x-x^2}} \, dx\)
3.843
\(\int \frac{1}{\sqrt{3-x} \sqrt{5+x}} \, dx\)
3.844
\(\int \frac{1}{\sqrt{(3-x) (5+x)}} \, dx\)
3.845
\(\int \frac{1}{\sqrt{-15-8 x-x^2}} \, dx\)
3.846
\(\int \frac{1}{\sqrt{-3-x} \sqrt{5+x}} \, dx\)
3.847
\(\int \frac{1}{\sqrt{(-3-x) (5+x)}} \, dx\)
3.848
\(\int (1-\sqrt{x}) \, dx\)
3.849
\(\int \frac{1-x}{1+\sqrt{x}} \, dx\)
3.850
\(\int \sqrt{\frac{1}{1-x^2}} \, dx\)
3.851
\(\int \sqrt{\frac{1+x^2}{1-x^4}} \, dx\)
3.852
\(\int \sqrt{\frac{1}{-1+x^2}} \, dx\)
3.853
\(\int \sqrt{\frac{1+x^2}{-1+x^4}} \, dx\)
3.854
\(\int \frac{1}{\sqrt{1-x}} \, dx\)
3.855
\(\int \frac{\sqrt{1+x}}{\sqrt{1-x^2}} \, dx\)
3.856
\(\int \frac{1}{\sqrt{1+x}} \, dx\)
3.857
\(\int \frac{\sqrt{1-x}}{\sqrt{1-x^2}} \, dx\)
3.858
\(\int \sqrt{1-x} \, dx\)
3.859
\(\int \frac{\sqrt{1-x^2}}{\sqrt{1+x}} \, dx\)
3.860
\(\int \sqrt{1+x} \, dx\)
3.861
\(\int \frac{\sqrt{1-x^2}}{\sqrt{1-x}} \, dx\)
3.862
\(\int \frac{\sqrt{2+3 x}}{\sqrt{1+x}} \, dx\)
3.863
\(\int \frac{\sqrt{1-x} \sqrt{2+3 x}}{\sqrt{1-x^2}} \, dx\)
3.864
\(\int \frac{(1+x)^{3/2}}{(1-x)^{3/2} x} \, dx\)
3.865
\(\int \frac{(1+x)^3}{x (1-x^2)^{3/2}} \, dx\)
3.866
\(\int \frac{(1+a x)^{3/2}}{x (1-a x)^{3/2}} \, dx\)
3.867
\(\int \frac{(1+a x)^3}{x (1-a^2 x^2)^{3/2}} \, dx\)
3.868
\(\int \frac{1}{\sqrt{1-x^2}} \, dx\)
3.869
\(\int \frac{\sqrt{1+x^2}}{\sqrt{1-x^4}} \, dx\)
3.870
\(\int \frac{1}{\sqrt{1+x^2}} \, dx\)
3.871
\(\int \frac{\sqrt{1-x^2}}{\sqrt{1-x^4}} \, dx\)
3.872
\(\int \sqrt{1-x^2} \, dx\)
3.873
\(\int \frac{\sqrt{1-x^4}}{\sqrt{1+x^2}} \, dx\)
3.874
\(\int \sqrt{1+x^2} \, dx\)
3.875
\(\int \frac{\sqrt{1-x^4}}{\sqrt{1-x^2}} \, dx\)
3.876
\(\int (\frac{a+b+c x^2}{d})^m \, dx\)
3.877
\(\int \frac{1}{x-\sqrt{1+x^2}} \, dx\)
3.878
\(\int \frac{1}{x-\sqrt{1-x^2}} \, dx\)
3.879
\(\int \frac{1}{x-\sqrt{1+2 x^2}} \, dx\)
3.880
\(\int \frac{2 x-x^3+x^2 \sqrt{2-x^2}}{-2+2 x^2} \, dx\)
3.881
\(\int \frac{x \sqrt{2-x^2}}{x-\sqrt{2-x^2}} \, dx\)
3.882
\(\int \frac{x}{-x+\sqrt{2 x-x^2}} \, dx\)
3.883
\(\int \frac{x+\sqrt{2 x-x^2}}{2-2 x} \, dx\)
3.884
\(\int \frac{\sqrt{2-x} \sqrt{x}+x}{2-2 x} \, dx\)
3.885
\(\int \frac{\sqrt{x}}{\sqrt{2-x}-\sqrt{x}} \, dx\)
3.886
\(\int \frac{1}{((1+x) (-1+x^2))^{2/3}} \, dx\)
3.887
\(\int \frac{-1+x^2}{(1+x^2) \sqrt{x (1+x^2)}} \, dx\)
3.888
\(\int \frac{-1+x^2}{(1+x^2) \sqrt{x+x^3}} \, dx\)
3.889
\(\int \frac{\sqrt{\frac{(-1+x^2)^2}{x (1+x^2)}}}{1+x^2} \, dx\)
3.890
\(\int \frac{\sqrt{\frac{(-1+x^2)^2}{x+x^3}}}{1+x^2} \, dx\)
3.891
\(\int \frac{1}{\sqrt{a+\frac{b}{x^2}} \sqrt{c+d x^2}} \, dx\)
3.892
\(\int \frac{\sqrt{-2 x^2+x^4}}{(-1+x^2) (2+x^2)} \, dx\)
3.893
\(\int \frac{\sqrt{1-\frac{1}{(-1+x^2)^2}}}{2-x^2} \, dx\)
3.894
\(\int \frac{\sqrt{\frac{-2 x^2+x^4}{(-1+x^2)^2}}}{2+x^2} \, dx\)
3.895
\(\int (1+\frac{2 x}{1+x^2})^{5/2} \, dx\)
3.896
\(\int (1+\frac{2 x}{1+x^2})^{3/2} \, dx\)
3.897
\(\int \sqrt{1+\frac{2 x}{1+x^2}} \, dx\)
3.898
\(\int \frac{1}{\sqrt{1+\frac{2 x}{1+x^2}}} \, dx\)
3.899
\(\int \frac{1}{(1+\frac{2 x}{1+x^2})^{3/2}} \, dx\)
3.900
\(\int \frac{\sqrt{1+\frac{2 x}{1+x^2}}}{1+x^2} \, dx\)
3.901
\(\int \sqrt{x-x^2} F(x) \, dx\)
3.902
\(\int \frac{F(x)}{\sqrt{x-x^2}} \, dx\)
3.903
\(\int \sqrt{1-x} \sqrt{x} F(x) \, dx\)
3.904
\(\int \frac{F(x)}{\sqrt{1-x} \sqrt{x}} \, dx\)
3.905
\(\int F(\frac{a+b x}{x}) \, dx\)
3.906
\(\int F(\frac{a+b x^2}{x^2}) \, dx\)
3.907
\(\int F(\frac{x}{a+b x}) \, dx\)
3.908
\(\int F(\frac{x^2}{a+b x^2}) \, dx\)
3.909
\(\int F(\frac{x^2}{(a+b x)^2}) \, dx\)
3.910
\(\int F(\frac{x^4}{(a+b x^2)^2}) \, dx\)
3.911
\(\int \frac{\sqrt{b x^2+\sqrt{a+b^2 x^4}}}{\sqrt{a+b^2 x^4}} \, dx\)
3.912
\(\int \frac{\sqrt{-b x^2+\sqrt{a+b^2 x^4}}}{\sqrt{a+b^2 x^4}} \, dx\)
3.913
\(\int \frac{\sqrt{2 x^2+\sqrt{3+4 x^4}}}{(c+d x) \sqrt{3+4 x^4}} \, dx\)
3.914
\(\int \frac{\sqrt{2 x^2+\sqrt{3+4 x^4}}}{(c+d x)^2 \sqrt{3+4 x^4}} \, dx\)
3.915
\(\int \frac{-4+x}{(1+\sqrt [3]{x}) \sqrt{x}} \, dx\)
3.916
\(\int \frac{1+\sqrt{x}}{x^{5/6}+x^{7/6}} \, dx\)
3.917
\(\int \frac{1+\sqrt{x}}{(1+\sqrt [3]{x}) \sqrt{x}} \, dx\)
3.918
\(\int \frac{\sqrt{2+\frac{b}{x^2}}}{b+2 x^2} \, dx\)
3.919
\(\int \frac{\sqrt{2-\frac{b}{x^2}}}{-b+2 x^2} \, dx\)
3.920
\(\int \frac{\sqrt{a+\frac{c}{x^2}}}{d+e x} \, dx\)
3.921
\(\int \frac{\sqrt{a+\frac{c}{x^2}+\frac{b}{x}}}{d+e x} \, dx\)
3.922
\(\int \frac{\sqrt [6]{x}+\sqrt [5]{x^3}}{\sqrt{x}} \, dx\)
3.923
\(\int \frac{2+x}{\sqrt{4 x-x^2}} \, dx\)
3.924
\(\int \frac{3+x}{\sqrt [3]{6 x+x^2}} \, dx\)
3.925
\(\int \frac{4+x}{(6 x-x^2)^{3/2}} \, dx\)
3.926
\(\int \frac{1}{(1+x) \sqrt{2 x+x^2}} \, dx\)
3.927
\(\int \frac{1}{(1+2 x) \sqrt{x+x^2}} \, dx\)
3.928
\(\int \frac{-1+x}{\sqrt{2 x-x^2}} \, dx\)
3.929
\(\int \frac{\sqrt{x-x^2}}{1+x} \, dx\)
3.930
\(\int \sqrt{\sqrt [4]{x}+x} \, dx\)
3.931
\(\int \sqrt{x+x^{3/2}} \, dx\)
3.932
\(\int x \sqrt{x+x^{3/2}} \, dx\)
3.933
\(\int (1-x^2) \sqrt{\frac{1}{2-x^2}} \, dx\)
3.934
\(\int \sqrt{x^2+x^3-x^4} \, dx\)
3.935
\(\int \frac{1}{\sqrt{(a^2+x^2)^3}} \, dx\)
3.936
\(\int \frac{\sqrt{x}}{1+\sqrt{x}+x} \, dx\)
3.937
\(\int \frac{x}{1+\sqrt{x}+x} \, dx\)
3.938
\(\int \frac{1}{\sqrt{x} (1+\sqrt{x}+x)^{7/2}} \, dx\)
3.939
\(\int \frac{-1+x}{1+\sqrt{1+x^2}} \, dx\)
3.940
\(\int \frac{1}{(1+x)^{2/3} (-1+x^2)^{2/3}} \, dx\)
3.941
\(\int ((1-x^6)^{2/3}+\frac{(1-x^6)^{2/3}}{x^6}) \, dx\)
3.942
\(\int \frac{x^{-1+m} (2 a m+b (2 m-n) x^n)}{2 (a+b x^n)^{3/2}} \, dx\)
3.943
\(\int \frac{x-2 x^3}{\sqrt{2+3 x}} \, dx\)
3.944
\(\int \frac{1}{\sqrt [4]{1+x}+\sqrt{1+x}} \, dx\)
3.945
\(\int \frac{1+2 x}{\sqrt{x+x^2}} \, dx\)
3.946
\(\int \frac{1}{2 \sqrt{x} (1+x)} \, dx\)
3.947
\(\int \frac{1}{x \sqrt{6 x-x^2}} \, dx\)
3.948
\(\int (1+\sqrt{x}) \sqrt{x} \, dx\)
3.949
\(\int \frac{1-\sqrt{x}}{\sqrt [3]{x}} \, dx\)
3.950
\(\int \frac{\sqrt{x}}{1+\sqrt [3]{x}} \, dx\)
3.951
\(\int \frac{\sqrt [3]{1+\sqrt{x}}}{x} \, dx\)
3.952
\(\int (1-\sqrt{x}) \, dx\)
3.953
\(\int (1-\sqrt [4]{x}) \, dx\)
3.954
\(\int \frac{1-\sqrt{x}}{1+\sqrt [4]{x}} \, dx\)
3.955
\(\int \frac{1}{\sqrt{(a+b x) (c+d x)}} \, dx\)
3.956
\(\int \frac{1}{\sqrt{(a+b x) (c-d x)}} \, dx\)
3.957
\(\int \frac{1}{\sqrt{x} (1-x^2)} \, dx\)
3.958
\(\int \frac{\sqrt{x}}{x-x^3} \, dx\)
3.959
\(\int \frac{x}{2-\sqrt{3}+(1+\sqrt{3}) x+x^2} \, dx\)
3.960
\(\int \sqrt{x^2+x^3} \, dx\)
3.961
\(\int \frac{1}{(1+x) \sqrt{2 x+x^2}} \, dx\)
3.962
\(\int \sqrt{1-\sqrt{x}-x} \sqrt{x} \, dx\)
3.963
\(\int \sqrt [3]{1+\sqrt{-3+x}} \, dx\)
3.964
\(\int \frac{1}{\sqrt{3+\sqrt{-1+2 x}}} \, dx\)
3.965
\(\int \frac{\sqrt{1-x}}{1+\sqrt{x}} \, dx\)
3.966
\(\int \frac{\sqrt{1-x}}{1-\sqrt{x}} \, dx\)
3.967
\(\int \frac{x}{x-\sqrt{1+x^2}} \, dx\)
3.968
\(\int \frac{x}{x-\sqrt{1-x^2}} \, dx\)
3.969
\(\int \frac{x}{x-\sqrt{1+2 x^2}} \, dx\)
3.970
\(\int \sqrt{x} \sqrt{\sqrt{x}+x} \, dx\)
3.971
\(\int \frac{1+\sqrt [3]{x}}{1+\sqrt{x}} \, dx\)
3.972
\(\int \frac{1+\sqrt [3]{x}}{1+\sqrt [4]{x}} \, dx\)
3.973
\(\int \frac{x^2}{-1+x^2+\sqrt{1-x^2}} \, dx\)
3.974
\(\int \sqrt{\frac{1+x}{x}} \, dx\)
3.975
\(\int \sqrt{\frac{1-x}{x}} \, dx\)
3.976
\(\int \sqrt{\frac{-1+x}{x}} \, dx\)
3.977
\(\int \frac{\sqrt{\frac{1+x}{x}}}{x} \, dx\)
3.978
\(\int \sqrt{\frac{x}{1+x}} \, dx\)
3.979
\(\int \frac{1}{\sqrt{\frac{-1-x}{x}}} \, dx\)
3.980
\(\int \sqrt{(4-x) x} \, dx\)
3.981
\(\int \frac{1}{\sqrt{(1-x) x}} \, dx\)
3.982
\(\int \frac{x}{(x (2+x))^{3/2}} \, dx\)
3.983
\(\int \frac{\sqrt{1+\frac{1}{x}}}{1-x^2} \, dx\)
3.984
\(\int \frac{1}{1+\sqrt{5}-x^2+\sqrt{5} x^2} \, dx\)
3.985
\(\int \frac{1}{\sqrt{a x+b x^2}} \, dx\)
3.986
\(\int \frac{1}{\sqrt{x (a+b x)}} \, dx\)
3.987
\(\int \frac{1}{\sqrt{(b+\frac{a}{x}) x^2}} \, dx\)
3.988
\(\int \frac{1}{\sqrt{(\frac{a}{x^2}+\frac{b}{x}) x^3}} \, dx\)
3.989
\(\int \frac{1}{\sqrt{\frac{a x^2+b x^3}{x}}} \, dx\)
3.990
\(\int \frac{1}{\sqrt{\frac{a x^3+b x^4}{x^2}}} \, dx\)
3.991
\(\int \frac{1}{\sqrt{a c x+b c x^2}} \, dx\)
3.992
\(\int \frac{1}{\sqrt{c (a x+b x^2)}} \, dx\)
3.993
\(\int \frac{1}{\sqrt{c x (a+b x)}} \, dx\)
3.994
\(\int \frac{1}{\sqrt{c (b+\frac{a}{x}) x^2}} \, dx\)
3.995
\(\int \sqrt{1-x^2+x \sqrt{-1+x^2}} \, dx\)
3.996
\(\int \frac{\sqrt{-x+\sqrt{x} \sqrt{1+x}}}{\sqrt{1+x}} \, dx\)
3.997
\(\int -\frac{x+2 \sqrt{1+x^2}}{x+x^3+\sqrt{1+x^2}} \, dx\)
3.998
\(\int \frac{1+2 x}{(1+x^2) \sqrt{2+2 x+x^2}} \, dx\)
3.999
\(\int \frac{1}{(1+x^4) \sqrt{-x^2+\sqrt{1+x^4}}} \, dx\)
3.1000
\(\int \frac{1}{(a+b x^4) \sqrt{c x^2+d \sqrt{a+b x^4}}} \, dx\)
3.1001
\(\int \frac{1}{(a+b x^4) \sqrt{-c x^2+d \sqrt{a+b x^4}}} \, dx\)
3.1002
\(\int \frac{x}{\sqrt{a+b c^4+4 b c^3 d x+6 b c^2 d^2 x^2+4 b c d^3 x^3+b d^4 x^4}} \, dx\)
3.1003
\(\int \frac{1}{\sqrt{a+b c^4+4 b c^3 d x+6 b c^2 d^2 x^2+4 b c d^3 x^3+b d^4 x^4}} \, dx\)
3.1004
\(\int \frac{a-c x^4}{\sqrt{a+b x^2+c x^4} (a d+a e x^2+c d x^4)} \, dx\)
3.1005
\(\int \frac{a-c x^4}{\sqrt{a-b x^2+c x^4} (a d+a e x^2+c d x^4)} \, dx\)
3.1006
\(\int \frac{1}{\sqrt{5-2 x+x^2} (8+x^3)} \, dx\)
3.1007
\(\int \sqrt{\frac{x^2}{1+x^2}} \, dx\)
3.1008
\(\int \sqrt{\frac{x^n}{1+x^n}} \, dx\)
3.1009
\(\int \frac{e f-e f x^2}{(a d+b d x+a d x^2) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx\)
3.1010
\(\int \frac{e f-e f x^2}{(-a d+b d x-a d x^2) \sqrt{-a+b x+c x^2+b x^3-a x^4}} \, dx\)
3.1011
\(\int \frac{\sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
3.1012
\(\int \frac{\sqrt{-a x^2+b x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
3.1013
\(\int \frac{\sqrt{x (a x+b \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}})}}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
3.1014
\(\int \frac{\sqrt{x (-a x+b \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}})}}{x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
3.1015
\(\int \frac{-\sqrt{-4+x}-4 \sqrt{-1+x}+\sqrt{-4+x} x+\sqrt{-1+x} x}{(1+\sqrt{-4+x}+\sqrt{-1+x}) (4-5 x+x^2)} \, dx\)
3.1016
\(\int \frac{1}{x (3+3 x+x^2) \sqrt [3]{3+3 x+3 x^2+x^3}} \, dx\)
3.1017
\(\int \frac{1-x^2}{(1-x+x^2) (1-x^3)^{2/3}} \, dx\)
3.1018
\(\int \frac{x^2}{\sqrt{-1+x^4} (1+x^4)} \, dx\)
3.1019
\(\int \frac{a-c x^4}{(a e+c d x^2) (d+e x^2) \sqrt{a+b x^2+c x^4}} \, dx\)
3.1020
\(\int (x+\frac{1-x^2}{1+x}) \, dx\)
3.1021
\(\int \frac{1}{\frac{1}{x}+\sqrt{1-x^2}} \, dx\)
3.1022
\(\int \frac{x \sqrt{1-x^2}}{x-x^3+\sqrt{1-x^2}} \, dx\)
3.1023
\(\int (1+x+x^2+x^3)^{-n} (1-x^4)^n \, dx\)
3.1024
\(\int \frac{x}{\sqrt{-44375 b^4+576000 b^3 c x+576000 b^2 c^2 x^2+5308416 c^4 x^4}} \, dx\)
3.1025
\(\int \frac{1+4 x}{\sqrt{9+120 x+64 x^2+64 x^3+64 x^4}} \, dx\)
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