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3
Listing of integrals
3.1
\(\int \cot ^4(x) \, dx\)
3.2
\(\int \frac{1}{x^4 \left (1+x^2\right )} \, dx\)
3.3
\(\int \frac{x+x^2}{\sqrt{x}} \, dx\)
3.4
\(\int \cos (x) \, dx\)
3.5
\(\int e^{x^2} x \, dx\)
3.6
\(\int \sec ^2(x) \tan (x) \, dx\)
3.7
\(\int x \sqrt{1+x^2} \, dx\)
3.8
\(\int e^x \sin (x) \, dx\)
3.9
\(\int \cot (x) \csc ^3(x) \, dx\)
3.10
\(\int \sin \left (e^x\right ) \, dx\)
3.11
\(\int \frac{\sin (y)}{y} \, dy\)
3.12
\(\int \left (e^x+\sin (x)\right ) \, dx\)
3.13
\(\int \left (e^{x^2}+2 e^{x^2} x^2\right ) \, dx\)
3.14
\(\int \left (e^x+x\right )^2 \, dx\)
3.15
\(\int \left (2 e^x+e^{2 x}+x^2\right ) \, dx\)
3.16
\(\int \cos (x) \sin (x) \, dx\)
3.17
\(\int e^{x^2} x \, dx\)
3.18
\(\int x \sqrt{1+x^2} \, dx\)
3.19
\(\int \frac{e^x}{1+e^x} \, dx\)
3.20
\(\int x^{3/2} \, dx\)
3.21
\(\int \cos (3+2 x) \, dx\)
3.22
\(\int 2 e^{2 x} y z \, dx\)
3.23
\(\int e^x \cos ^2\left (e^x\right ) \sin \left (e^x\right ) \, dx\)
3.24
\(\int x \sqrt{1+x} \, dx\)
3.25
\(\int \frac{1}{-1+x^4} \, dx\)
3.26
\(\int \frac{e^x}{2+3 e^{2 x}} \, dx\)
3.27
\(\int \frac{e^{2 x}}{A+B e^{4 x}} \, dx\)
3.28
\(\int \frac{e^{1+x}}{1+e^x} \, dx\)
3.29
\(\int (10 e)^x \, dx\)
3.30
\(\int x^3 \sin \left (x^2\right ) \, dx\)
3.31
\(\int \frac{x^7}{1+x^{12}} \, dx\)
3.32
\(\int x^{3 a} \sin \left (x^{2 a}\right ) \, dx\)
3.33
\(\int \cos \left (\sqrt{x}\right ) \, dx\)
3.34
\(\int x \sqrt{1+x} \, dx\)
3.35
\(\int \frac{1}{\sqrt [3]{x}+\sqrt{x}} \, dx\)
3.36
\(\int \sqrt{\frac{1+x}{3+2 x}} \, dx\)
3.37
\(\int \frac{x^4}{\left (1-x^2\right )^{5/2}} \, dx\)
3.38
\(\int \sqrt{x} (1+x)^{5/2} \, dx\)
3.39
\(\int \frac{x^4}{\left (1-x^2\right )^{5/2}} \, dx\)
3.40
\(\int \frac{\sqrt{A^2+B^2-B^2 y^2}}{1-y^2} \, dy\)
3.41
\(\int \sin ^2(x) \, dx\)
3.42
\(\int \csc (x) \sqrt{A^2+B^2 \sin ^2(x)} \, dx\)
3.43
\(\int \frac{1}{1+\cos (x)} \, dx\)
3.44
\(\int e^x x \, dx\)
3.45
\(\int \frac{e^x x}{(1+x)^2} \, dx\)
3.46
\(\int e^{x^2} \left (1+2 x^2\right ) \, dx\)
3.47
\(\int e^{x^2} \, dx\)
3.48
\(\int \frac{e^x}{x} \, dx\)
3.49
\(\int \frac{x}{1+x^3} \, dx\)
3.50
\(\int \frac{1}{-1+x^6} \, dx\)
3.51
\(\int \frac{1}{A^4-A^2 B^2+\left (-A^2+B^2\right ) x^2} \, dx\)
3.52
\(\int x \log (x) \, dx\)
3.53
\(\int x^2 \sin ^{-1}(x) \, dx\)
3.54
\(\int \frac{1}{1+2 x+x^2} \, dx\)
3.55
\(\int \frac{\log (x)}{(1+\log (x))^2} \, dx\)
3.56
\(\int \frac{1}{x \left (1+\log ^2(x)\right )} \, dx\)
3.57
\(\int \frac{1}{\log (x)} \, dx\)
3.58
\(\int x (\cos (x)+\sin (x)) \, dx\)
3.59
\(\int e^{-x} \left (e^x+x\right ) \, dx\)
3.60
\(\int \left (1+e^x\right )^2 x \, dx\)
3.61
\(\int x \cos (x) \, dx\)
3.62
\(\int \cos \left (\sqrt{x}\right ) \, dx\)
3.63
\(\int x \cos (x) \, dx\)
3.64
\(\int x \log ^2(x) \, dx\)
3.65
\(\int \cos (x) \left (1+\sin ^3(x)\right ) \, dx\)
3.66
\(\int \frac{1}{x \left (1+\log ^2(x)\right )} \, dx\)
3.67
\(\int \frac{1}{\sqrt{1-x^2} \left (1+\sin ^{-1}(x)^2\right )} \, dx\)
3.68
\(\int \frac{\sin (x)}{\cos (x)+\sin (x)} \, dx\)
3.69
\(\int -\frac{\sqrt{A^2+B^2 \left (1-y^2\right )}}{1-y^2} \, dy\)
3.70
\(\int \frac{\left (-A^2-B^2\right ) \cos ^2(z)}{B \left (1-\frac{\left (A^2+B^2\right ) \sin ^2(z)}{B^2}\right )} \, dz\)
3.71
\(\int -\frac{A^2+B^2}{B \left (1+w^2\right )^2 \left (1-\frac{\left (A^2+B^2\right ) w^2}{B^2 \left (1+w^2\right )}\right )} \, dw\)
3.72
\(\int -\frac{B \left (A^2+B^2\right )}{\left (1+w^2\right ) \left (B^2-A^2 w^2\right )} \, dw\)
3.73
\(\int \frac{x^4}{\left (1-x^2\right )^{5/2}} \, dx\)
3.74
\(\int \tan ^4(y) \, dy\)
3.75
\(\int \frac{z^4}{1+z^2} \, dz\)
3.76
\(\int e^{x^2} \left (1+2 x^2\right ) \, dx\)
3.77
\(\int \frac{e^{x^2} \left (1+4 x^2+x^3+5 x^4+2 x^6\right )}{\left (1+x^2\right )^2} \, dx\)
3.78
\(\int e^{-1-x} \, dx\)
3.79
\(\int \left (\frac{1}{x}+x\right ) \log (x) \, dx\)
3.80
\(\int \frac{x}{1+x^4} \, dx\)
3.81
\(\int \frac{x^5}{1+x^4} \, dx\)
3.82
\(\int \frac{1}{1+\tan ^2(x)} \, dx\)
3.83
\(\int \frac{x^4}{\left (1-x^2\right )^{5/2}} \, dx\)
3.84
\(\int -\frac{x^2}{\left (1-x^2\right )^{3/2}} \, dx\)
3.85
\(\int e^x \sin (x) \, dx\)
3.86
\(\int \frac{1}{x} \, dx\)
3.87
\(\int \frac{\sec (2 t)}{1+\sec ^2(t)+3 \tan (t)} \, dt\)
3.88
\(\int \cos ^2(x) \, dx\)
3.89
\(\int \frac{1+x^2}{\sqrt{x}} \, dx\)
3.90
\(\int \frac{x}{\sqrt{5+2 x+x^2}} \, dx\)
3.91
\(\int \cos (x) \sin ^2(x) \, dx\)
3.92
\(\int \frac{e^x}{1+e^x} \, dx\)
3.93
\(\int \frac{e^{2 x}}{1+e^x} \, dx\)
3.94
\(\int \frac{1}{1-\cos (x)} \, dx\)
3.95
\(\int \sec ^2(x) \tan (x) \, dx\)
3.96
\(\int x \log (x) \, dx\)
3.97
\(\int \cos (x) \sin (x) \, dx\)
3.98
\(\int \frac{1+x}{\sqrt{2 x-x^2}} \, dx\)
3.99
\(\int \frac{2 e^x}{2+3 e^{2 x}} \, dx\)
3.100
\(\int \frac{x^4}{\left (1-x^2\right )^{5/2}} \, dx\)
3.101
\(\int \frac{e^{6 x}}{1+e^{4 x}} \, dx\)
3.102
\(\int \log \left (2+3 x^2\right ) \, dx\)
3.103
\(\int \frac{1}{r \sqrt{-a^2+2 H r^2}} \, dx\)
3.104
\(\int \frac{1}{r \sqrt{-a^2-e^2+2 H r^2}} \, dx\)
3.105
\(\int \frac{1}{r \sqrt{-a^2+2 H r^2-2 K r^4}} \, dx\)
3.106
\(\int \frac{1}{r \sqrt{-a^2-e^2+2 H r^2-2 K r^4}} \, dx\)
3.107
\(\int \frac{1}{r \sqrt{-a^2-2 K r+2 H r^2}} \, dx\)
3.108
\(\int \frac{1}{r \sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx\)
3.109
\(\int \frac{r}{\sqrt{-a^2+2 e r^2}} \, dx\)
3.110
\(\int \frac{r}{\sqrt{-a^2-e^2+2 e r^2}} \, dx\)
3.111
\(\int \frac{r}{\sqrt{-a^2+2 e r^2-2 K r^4}} \, dx\)
3.112
\(\int \frac{r}{\sqrt{-a^2-e^2+2 e r^2-2 K r^4}} \, dx\)
3.113
\(\int \frac{r}{\sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx\)
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