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Chapter 3
Listing of integrals
3.1
\(\int \sqrt{1+2 x} \, dx\)
3.2
\(\int x \sqrt{1+3 x} \, dx\)
3.3
\(\int x^2 \sqrt{1+x} \, dx\)
3.4
\(\int \frac{x}{\sqrt{2-3 x}} \, dx\)
3.5
\(\int \frac{1+x}{(2+2 x+x^2)^3} \, dx\)
3.6
\(\int \sin ^3(x) \, dx\)
3.7
\(\int \sqrt [3]{-1+z} z \, dz\)
3.8
\(\int \cot (x) \csc ^2(x) \, dx\)
3.9
\(\int \cos (2 x) \sqrt{4-\sin (2 x)} \, dx\)
3.10
\(\int \frac{\sin (x)}{(3+\cos (x))^2} \, dx\)
3.11
\(\int \frac{\sin (x)}{\sqrt{\cos ^3(x)}} \, dx\)
3.12
\(\int \frac{\sin (\sqrt{1+x})}{\sqrt{1+x}} \, dx\)
3.13
\(\int x^{-1+n} \sin (x^n) \, dx\)
3.14
\(\int \frac{x^5}{\sqrt{1-x^6}} \, dx\)
3.15
\(\int t \sqrt [4]{1+t} \, dt\)
3.16
\(\int \frac{1}{(1+x^2)^{3/2}} \, dx\)
3.17
\(\int x^2 (27+8 x^3)^{2/3} \, dx\)
3.18
\(\int \frac{\cos (x)+\sin (x)}{\sqrt [3]{-\cos (x)+\sin (x)}} \, dx\)
3.19
\(\int \frac{x}{\sqrt{1+x^2+(1+x^2)^{3/2}}} \, dx\)
3.20
\(\int \frac{x}{\sqrt{1+x^2} \sqrt{1+\sqrt{1+x^2}}} \, dx\)
3.21
\(\int \frac{\sqrt [5]{1-2 x+x^2}}{1-x} \, dx\)
3.22
\(\int x \sin (x) \, dx\)
3.23
\(\int x^2 \sin (x) \, dx\)
3.24
\(\int x^3 \cos (x) \, dx\)
3.25
\(\int x^3 \sin (x) \, dx\)
3.26
\(\int \cos (x) \sin (x) \, dx\)
3.27
\(\int x \cos (x) \sin (x) \, dx\)
3.28
\(\int \sin ^2(x) \, dx\)
3.29
\(\int \sin ^3(x) \, dx\)
3.30
\(\int \sin ^4(x) \, dx\)
3.31
\(\int \sin ^5(x) \, dx\)
3.32
\(\int \sin ^6(x) \, dx\)
3.33
\(\int x \sin ^2(x) \, dx\)
3.34
\(\int x \sin ^3(x) \, dx\)
3.35
\(\int x^2 \sin ^2(x) \, dx\)
3.36
\(\int \cos ^2(x) \, dx\)
3.37
\(\int \cos ^3(x) \, dx\)
3.38
\(\int \cos ^4(x) \, dx\)
3.39
\(\int (a^2-x^2)^{5/2} \, dx\)
3.40
\(\int \frac{x^5}{\sqrt{5+x^2}} \, dx\)
3.41
\(\int \frac{t^3}{\sqrt{4+t^3}} \, dt\)
3.42
\(\int \tan ^2(x) \, dx\)
3.43
\(\int \tan ^4(x) \, dx\)
3.44
\(\int \cot ^2(x) \, dx\)
3.45
\(\int \cot ^4(x) \, dx\)
3.46
\(\int (2+3 x) \sin (5 x) \, dx\)
3.47
\(\int x \sqrt{1+x^2} \, dx\)
3.48
\(\int x (-1+x^2)^9 \, dx\)
3.49
\(\int \frac{3+2 x}{(7+6 x)^3} \, dx\)
3.50
\(\int x^4 (1+x^5)^5 \, dx\)
3.51
\(\int (1-x)^{20} x^4 \, dx\)
3.52
\(\int \frac{\sin (\frac{1}{x})}{x^2} \, dx\)
3.53
\(\int \sin (\sqrt [4]{-1+x}) \, dx\)
3.54
\(\int x \cos (x^2) \sin (x^2) \, dx\)
3.55
\(\int \sqrt{1+3 \cos ^2(x)} \sin (2 x) \, dx\)
3.56
\(\int \frac{1}{2+3 x} \, dx\)
3.57
\(\int \log ^2(x) \, dx\)
3.58
\(\int x \log (x) \, dx\)
3.59
\(\int x \log ^2(x) \, dx\)
3.60
\(\int \frac{1}{1+t} \, dt\)
3.61
\(\int \cot (x) \, dx\)
3.62
\(\int x^n \log (a x) \, dx\)
3.63
\(\int x^2 \log ^2(x) \, dx\)
3.64
\(\int \frac{1}{x \log (x)} \, dx\)
3.65
\(\int \frac{\log (1-t)}{1-t} \, dt\)
3.66
\(\int \frac{\log (x)}{x \sqrt{1+\log (x)}} \, dx\)
3.67
\(\int x^3 \log ^3(x) \, dx\)
3.68
\(\int e^{x^3} x^2 \, dx\)
3.69
\(\int \frac{2^{\sqrt{x}}}{\sqrt{x}} \, dx\)
3.70
\(\int e^{2 \sin (x)} \cos (x) \, dx\)
3.71
\(\int e^x \sin (x) \, dx\)
3.72
\(\int e^x \cos (x) \, dx\)
3.73
\(\int \frac{1}{1+e^x} \, dx\)
3.74
\(\int e^x x \, dx\)
3.75
\(\int e^{-x} x \, dx\)
3.76
\(\int e^x x^2 \, dx\)
3.77
\(\int e^{-2 x} x^2 \, dx\)
3.78
\(\int e^{\sqrt{x}} \, dx\)
3.79
\(\int e^{-x^2} x^3 \, dx\)
3.80
\(\int e^{a x} \cos (b x) \, dx\)
3.81
\(\int e^{a x} \sin (b x) \, dx\)
3.82
\(\int \cot ^{-1}(x) \, dx\)
3.83
\(\int \sec ^{-1}(x) \, dx\)
3.84
\(\int \csc ^{-1}(x) \, dx\)
3.85
\(\int \sin ^{-1}(x)^2 \, dx\)
3.86
\(\int \frac{\sin ^{-1}(x)}{x^2} \, dx\)
3.87
\(\int \frac{1}{\sqrt{a^2-x^2}} \, dx\)
3.88
\(\int \frac{1}{\sqrt{1-2 x-x^2}} \, dx\)
3.89
\(\int \frac{1}{a^2+x^2} \, dx\)
3.90
\(\int \frac{1}{a+b x^2} \, dx\)
3.91
\(\int \frac{1}{2-x+x^2} \, dx\)
3.92
\(\int x \tan ^{-1}(x) \, dx\)
3.93
\(\int x^2 \cos ^{-1}(x) \, dx\)
3.94
\(\int x \tan ^{-1}(x)^2 \, dx\)
3.95
\(\int \tan ^{-1}(\sqrt{x}) \, dx\)
3.96
\(\int \frac{\tan ^{-1}(\sqrt{x})}{\sqrt{x} (1+x)} \, dx\)
3.97
\(\int \sqrt{1-x^2} \, dx\)
3.98
\(\int \frac{e^{\tan ^{-1}(x)} x}{(1+x^2)^{3/2}} \, dx\)
3.99
\(\int \frac{e^{\tan ^{-1}(x)}}{(1+x^2)^{3/2}} \, dx\)
3.100
\(\int \frac{x^2}{(1+x^2)^2} \, dx\)
3.101
\(\int \frac{e^x}{1+e^{2 x}} \, dx\)
3.102
\(\int e^{-x} \cot ^{-1}(e^x) \, dx\)
3.103
\(\int \sqrt{\frac{a+x}{a-x}} \, dx\)
3.104
\(\int \sqrt{(b-x) (-a+x)} \, dx\)
3.105
\(\int \frac{1}{\sqrt{(b-x) (-a+x)}} \, dx\)
3.106
\(\int \frac{3+5 x}{-3+2 x+x^2} \, dx\)
3.107
\(\int \frac{5+2 x}{-3+2 x+x^2} \, dx\)
3.108
\(\int \frac{3 x+x^3}{-3-2 x+x^2} \, dx\)
3.109
\(\int \frac{-1+5 x+2 x^2}{-2 x+x^2+x^3} \, dx\)
3.110
\(\int \frac{3+2 x+x^2}{(-1+x) (1+x)^2} \, dx\)
3.111
\(\int \frac{-2+2 x+3 x^2}{-1+x^3} \, dx\)
3.112
\(\int \frac{2-x+2 x^2-x^3+x^4}{(-1+x) (2+x^2)^2} \, dx\)
3.113
\(\int \frac{1}{\cos (x)+\sin (x)} \, dx\)
3.114
\(\int \frac{x}{4-x^2+\sqrt{4-x^2}} \, dx\)
3.115
\(\int \frac{3+2 x}{(-2+x) (5+x)} \, dx\)
3.116
\(\int \frac{x}{(1+x) (2+x) (3+x)} \, dx\)
3.117
\(\int \frac{x}{2-3 x+x^3} \, dx\)
3.118
\(\int \frac{-6+2 x+x^4}{-2 x+x^2+x^3} \, dx\)
3.119
\(\int \frac{7+8 x^3}{(1+x) (1+2 x)^3} \, dx\)
3.120
\(\int \frac{1+x+4 x^2}{-1+x^3} \, dx\)
3.121
\(\int \frac{x^4}{4+5 x^2+x^4} \, dx\)
3.122
\(\int \frac{2+x}{x+x^2} \, dx\)
3.123
\(\int \frac{1}{x (1+x^2)^2} \, dx\)
3.124
\(\int \frac{1}{(1+x) (2+x)^2 (3+x)^3} \, dx\)
3.125
\(\int \frac{x}{(1+x)^2} \, dx\)
3.126
\(\int \frac{1}{-x+x^3} \, dx\)
3.127
\(\int \frac{x^2}{-6+x+x^2} \, dx\)
3.128
\(\int \frac{2+x}{4-4 x+x^2} \, dx\)
3.129
\(\int \frac{1}{(4-4 x+x^2) (5-4 x+x^2)} \, dx\)
3.130
\(\int \frac{-3+x}{2 x+3 x^2+x^3} \, dx\)
3.131
\(\int \frac{1}{(-1+x^2)^2} \, dx\)
3.132
\(\int \frac{1+x}{-1+x^3} \, dx\)
3.133
\(\int \frac{1+x^4}{x (1+x^2)^2} \, dx\)
3.134
\(\int \frac{1}{-2 x^3+x^4} \, dx\)
3.135
\(\int \frac{1-x^3}{x (1+x^2)} \, dx\)
3.136
\(\int \frac{1}{-1+x^4} \, dx\)
3.137
\(\int \frac{1}{1+x^4} \, dx\)
3.138
\(\int \frac{x^2}{(2+2 x+x^2)^2} \, dx\)
3.139
\(\int \frac{-1+4 x^5}{(1+x+x^5)^2} \, dx\)
3.140
\(\int \frac{1}{5-\cos (x)+2 \sin (x)} \, dx\)
3.141
\(\int \frac{1}{1+a \cos (x)} \, dx\)
3.142
\(\int \frac{1}{1+2 \cos (x)} \, dx\)
3.143
\(\int \frac{1}{1+\frac{\cos (x)}{2}} \, dx\)
3.144
\(\int \frac{\sin ^2(x)}{1+\sin ^2(x)} \, dx\)
3.145
\(\int \frac{1}{b^2 \cos ^2(x)+a^2 \sin ^2(x)} \, dx\)
3.146
\(\int \frac{1}{(b \cos (x)+a \sin (x))^2} \, dx\)
3.147
\(\int \frac{\sin (x)}{1+\cos (x)+\sin (x)} \, dx\)
3.148
\(\int \sqrt{3-x^2} \, dx\)
3.149
\(\int \frac{x}{\sqrt{3-x^2}} \, dx\)
3.150
\(\int \frac{\sqrt{3-x^2}}{x} \, dx\)
3.151
\(\int \frac{\sqrt{x+x^2}}{x} \, dx\)
3.152
\(\int \sqrt{5+x^2} \, dx\)
3.153
\(\int \frac{x}{\sqrt{1+x+x^2}} \, dx\)
3.154
\(\int \frac{1}{\sqrt{x+x^2}} \, dx\)
3.155
\(\int \frac{\sqrt{2-x-x^2}}{x^2} \, dx\)
3.156
\(\int \frac{\log (t)}{1+t} \, dt\)
3.157
\(\int \log (e^{\cos (x)}) \, dx\)
3.158
\(\int \frac{e^t}{t} \, dt\)
3.159
\(\int \frac{e^{a t}}{t} \, dt\)
3.160
\(\int \frac{e^t}{t^2} \, dt\)
3.161
\(\int e^{\frac{1}{t}} \, dt\)
3.162
\(\int \frac{e^{-t}}{-1-a+t} \, dt\)
3.163
\(\int \frac{e^{t^2} t}{1+t^2} \, dt\)
3.164
\(\int \frac{e^t}{(1+t)^2} \, dt\)
3.165
\(\int e^t \log (1+t) \, dt\)
3.166
\(\int e^{-t} t \, dt\)
3.167
\(\int e^{-t} t^2 \, dt\)
3.168
\(\int e^{-t} t^3 \, dt\)
3.169
\(\int \frac{\text{b1} \cos (x)+\text{a1} \sin (x)}{b \cos (x)+a \sin (x)} \, dx\)
3.170
\(\int \frac{1}{\log (t)} \, dt\)
3.171
\(\int \frac{1}{\log ^2(t)} \, dt\)
3.172
\(\int \log ^{-1-n}(t) \, dt\)
3.173
\(\int \frac{e^{2 t}}{-1+t} \, dt\)
3.174
\(\int \frac{e^{2 x}}{2-3 x+x^2} \, dx\)
3.175
\(\int \frac{1}{\sqrt{1+t^3}} \, dt\)
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