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3
Listing of integrals
3.1
\(\int (d+e x) \left (a+b x^2+c x^4\right ) \, dx\)
3.2
\(\int \left (d+e x+f x^2\right ) \left (a+b x^2+c x^4\right ) \, dx\)
3.3
\(\int \left (d+e x+f x^2+g x^3\right ) \left (a+b x^2+c x^4\right ) \, dx\)
3.4
\(\int \left (a+b x^2+c x^4\right ) \left (d+e x+f x^2+g x^3+h x^4\right ) \, dx\)
3.5
\(\int \left (a+b x^2+c x^4\right ) \left (d+e x+f x^2+g x^3+h x^4+i x^5\right ) \, dx\)
3.6
\(\int (d+e x) \left (a+b x^2+c x^4\right )^2 \, dx\)
3.7
\(\int \left (d+e x+f x^2\right ) \left (a+b x^2+c x^4\right )^2 \, dx\)
3.8
\(\int \left (d+e x+f x^2+g x^3\right ) \left (a+b x^2+c x^4\right )^2 \, dx\)
3.9
\(\int \left (a+b x^2+c x^4\right )^2 \left (d+e x+f x^2+g x^3+h x^4\right ) \, dx\)
3.10
\(\int \frac{d+e x}{4-5 x^2+x^4} \, dx\)
3.11
\(\int \frac{d+e x+f x^2}{4-5 x^2+x^4} \, dx\)
3.12
\(\int \frac{d+e x+f x^2+g x^3}{4-5 x^2+x^4} \, dx\)
3.13
\(\int \frac{d+e x+f x^2+g x^3+h x^4}{4-5 x^2+x^4} \, dx\)
3.14
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{4-5 x^2+x^4} \, dx\)
3.15
\(\int \frac{d+e x}{1+x^2+x^4} \, dx\)
3.16
\(\int \frac{d+e x+f x^2}{1+x^2+x^4} \, dx\)
3.17
\(\int \frac{d+e x+f x^2+g x^3}{1+x^2+x^4} \, dx\)
3.18
\(\int \frac{d+e x+f x^2+g x^3+h x^4}{1+x^2+x^4} \, dx\)
3.19
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{1+x^2+x^4} \, dx\)
3.20
\(\int \frac{d+e x}{a+b x^2+c x^4} \, dx\)
3.21
\(\int \frac{d+e x+f x^2}{a+b x^2+c x^4} \, dx\)
3.22
\(\int \frac{d+e x+f x^2+g x^3}{a+b x^2+c x^4} \, dx\)
3.23
\(\int \frac{d+e x+f x^2+g x^3+h x^4}{a+b x^2+c x^4} \, dx\)
3.24
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{a+b x^2+c x^4} \, dx\)
3.25
\(\int \frac{d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{a+b x^2+c x^4} \, dx\)
3.26
\(\int \frac{d+e x}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.27
\(\int \frac{d+e x+f x^2}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.28
\(\int \frac{d+e x+f x^2+g x^3}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.29
\(\int \frac{d+e x+f x^2+g x^3+h x^4}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.30
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.31
\(\int \frac{d+e x}{\left (1+x^2+x^4\right )^2} \, dx\)
3.32
\(\int \frac{d+e x+f x^2}{\left (1+x^2+x^4\right )^2} \, dx\)
3.33
\(\int \frac{d+e x+f x^2+g x^3}{\left (1+x^2+x^4\right )^2} \, dx\)
3.34
\(\int \frac{d+e x+f x^2+g x^3+h x^4}{\left (1+x^2+x^4\right )^2} \, dx\)
3.35
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left (1+x^2+x^4\right )^2} \, dx\)
3.36
\(\int \frac{d+e x}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.37
\(\int \frac{d+e x+f x^2}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.38
\(\int \frac{d+e x+f x^2+g x^3}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.39
\(\int \frac{d+e x+f x^2+g x^3+h x^4}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.40
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.41
\(\int \frac{d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.42
\(\int \frac{d+e x}{\left (4-5 x^2+x^4\right )^3} \, dx\)
3.43
\(\int \frac{d+e x+f x^2}{\left (4-5 x^2+x^4\right )^3} \, dx\)
3.44
\(\int \frac{d+e x+f x^2+g x^3}{\left (4-5 x^2+x^4\right )^3} \, dx\)
3.45
\(\int \frac{d+e x+f x^2+g x^3+h x^4}{\left (4-5 x^2+x^4\right )^3} \, dx\)
3.46
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left (4-5 x^2+x^4\right )^3} \, dx\)
3.47
\(\int \frac{d+e x}{\left (1+x^2+x^4\right )^3} \, dx\)
3.48
\(\int \frac{d+e x+f x^2}{\left (1+x^2+x^4\right )^3} \, dx\)
3.49
\(\int \frac{d+e x+f x^2+g x^3}{\left (1+x^2+x^4\right )^3} \, dx\)
3.50
\(\int \frac{d+e x+f x^2+g x^3+h x^4}{\left (1+x^2+x^4\right )^3} \, dx\)
3.51
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left (1+x^2+x^4\right )^3} \, dx\)
3.52
\(\int \frac{d+e x}{\left (a+b x^2+c x^4\right )^3} \, dx\)
3.53
\(\int \frac{d+e x+f x^2}{\left (a+b x^2+c x^4\right )^3} \, dx\)
3.54
\(\int \frac{d+e x+f x^2+g x^3}{\left (a+b x^2+c x^4\right )^3} \, dx\)
3.55
\(\int \frac{d+e x+f x^2+g x^3+h x^4}{\left (a+b x^2+c x^4\right )^3} \, dx\)
3.56
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left (a+b x^2+c x^4\right )^3} \, dx\)
3.57
\(\int \frac{d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{\left (a+b x^2+c x^4\right )^3} \, dx\)
3.58
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5+j x^6+k x^7}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.59
\(\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5+j x^8+k x^{11}}{\left (a+b x^2+c x^4\right )^3} \, dx\)
3.60
\(\int \left (a+b x^2+c x^4\right )^3 \left (a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6\right ) \, dx\)
3.61
\(\int \left (a+b x^2+c x^4\right )^2 \left (a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6\right ) \, dx\)
3.62
\(\int \left (a+b x^2+c x^4\right ) \left (a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6\right ) \, dx\)
3.63
\(\int \frac{a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{a+b x^2+c x^4} \, dx\)
3.64
\(\int \frac{a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{\left (a+b x^2+c x^4\right )^2} \, dx\)
3.65
\(\int \frac{a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{\left (a+b x^2+c x^4\right )^3} \, dx\)
3.66
\(\int \frac{a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{\left (a+b x^2+c x^4\right )^4} \, dx\)
3.67
\(\int \frac{2-x-2 x^2+x^3}{4-5 x^2+x^4} \, dx\)
3.68
\(\int \frac{(d+e x) \left (2-x-2 x^2+x^3\right )}{4-5 x^2+x^4} \, dx\)
3.69
\(\int \frac{\left (d+e x+f x^2\right ) \left (2-x-2 x^2+x^3\right )}{4-5 x^2+x^4} \, dx\)
3.70
\(\int \frac{\left (2-x-2 x^2+x^3\right ) \left (d+e x+f x^2+g x^3\right )}{4-5 x^2+x^4} \, dx\)
3.71
\(\int \frac{\left (2-x-2 x^2+x^3\right ) \left (d+e x+f x^2+g x^3+h x^4\right )}{4-5 x^2+x^4} \, dx\)
3.72
\(\int \frac{\left (2-x-2 x^2+x^3\right ) \left (d+e x+f x^2+g x^3+h x^4+i x^5\right )}{4-5 x^2+x^4} \, dx\)
3.73
\(\int \frac{2-3 x+x^2}{4-5 x^2+x^4} \, dx\)
3.74
\(\int \frac{(d+e x) \left (2-3 x+x^2\right )}{4-5 x^2+x^4} \, dx\)
3.75
\(\int \frac{\left (2-3 x+x^2\right ) \left (d+e x+f x^2\right )}{4-5 x^2+x^4} \, dx\)
3.76
\(\int \frac{\left (2-3 x+x^2\right ) \left (d+e x+f x^2+g x^3\right )}{4-5 x^2+x^4} \, dx\)
3.77
\(\int \frac{\left (2-3 x+x^2\right ) \left (d+e x+f x^2+g x^3+h x^4\right )}{4-5 x^2+x^4} \, dx\)
3.78
\(\int \frac{\left (2-3 x+x^2\right ) \left (d+e x+f x^2+g x^3+h x^4+i x^5\right )}{4-5 x^2+x^4} \, dx\)
3.79
\(\int \frac{2+x}{4-5 x^2+x^4} \, dx\)
3.80
\(\int \frac{(2+x) (d+e x)}{4-5 x^2+x^4} \, dx\)
3.81
\(\int \frac{(2+x) \left (d+e x+f x^2\right )}{4-5 x^2+x^4} \, dx\)
3.82
\(\int \frac{(2+x) \left (d+e x+f x^2+g x^3\right )}{4-5 x^2+x^4} \, dx\)
3.83
\(\int \frac{(2+x) \left (d+e x+f x^2+g x^3+h x^4\right )}{4-5 x^2+x^4} \, dx\)
3.84
\(\int \frac{(2+x) \left (d+e x+f x^2+g x^3+h x^4+i x^5\right )}{4-5 x^2+x^4} \, dx\)
3.85
\(\int \frac{2-x-2 x^2+x^3}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.86
\(\int \frac{(d+e x) \left (2-x-2 x^2+x^3\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.87
\(\int \frac{\left (d+e x+f x^2\right ) \left (2-x-2 x^2+x^3\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.88
\(\int \frac{\left (2-x-2 x^2+x^3\right ) \left (d+e x+f x^2+g x^3\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.89
\(\int \frac{\left (2-x-2 x^2+x^3\right ) \left (d+e x+f x^2+g x^3+h x^4\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.90
\(\int \frac{\left (2-x-2 x^2+x^3\right ) \left (d+e x+f x^2+g x^3+h x^4+i x^5\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.91
\(\int \frac{2-3 x+x^2}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.92
\(\int \frac{(d+e x) \left (2-3 x+x^2\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.93
\(\int \frac{\left (2-3 x+x^2\right ) \left (d+e x+f x^2\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.94
\(\int \frac{\left (2-3 x+x^2\right ) \left (d+e x+f x^2+g x^3\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.95
\(\int \frac{\left (2-3 x+x^2\right ) \left (d+e x+f x^2+g x^3+h x^4\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.96
\(\int \frac{\left (2-3 x+x^2\right ) \left (d+e x+f x^2+g x^3+h x^4+i x^5\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.97
\(\int \frac{2+x}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.98
\(\int \frac{(2+x) (d+e x)}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.99
\(\int \frac{(2+x) \left (d+e x+f x^2\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.100
\(\int \frac{(2+x) \left (d+e x+f x^2+g x^3\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.101
\(\int \frac{(2+x) \left (d+e x+f x^2+g x^3+h x^4\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.102
\(\int \frac{(2+x) \left (d+e x+f x^2+g x^3+h x^4+i x^5\right )}{\left (4-5 x^2+x^4\right )^2} \, dx\)
3.103
\(\int \left (d+e x+f x^2+g x^3\right ) \left (a+b x^2+c x^4\right )^{3/2} \, dx\)
3.104
\(\int \left (d+e x+f x^2+g x^3\right ) \sqrt{a+b x^2+c x^4} \, dx\)
3.105
\(\int \frac{d+e x+f x^2+g x^3}{\sqrt{a+b x^2+c x^4}} \, dx\)
3.106
\(\int \frac{d+e x+f x^2+g x^3}{\left (a+b x^2+c x^4\right )^{3/2}} \, dx\)
3.107
\(\int \frac{d+e x+f x^2+g x^3}{\left (a+b x^2+c x^4\right )^{5/2}} \, dx\)
3.108
\(\int \frac{a g-c g x^4}{\left (a+b x^2+c x^4\right )^{3/2}} \, dx\)
3.109
\(\int \frac{a g+e x-c g x^4}{\left (a+b x^2+c x^4\right )^{3/2}} \, dx\)
3.110
\(\int \frac{a g+f x^3-c g x^4}{\left (a+b x^2+c x^4\right )^{3/2}} \, dx\)
3.111
\(\int \frac{a g+e x+f x^3-c g x^4}{\left (a+b x^2+c x^4\right )^{3/2}} \, dx\)
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