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3.6
Integrals 501 to 594
3.6.1
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) \sqrt {a+b x^4}}{x^2} \, dx\) [501]
3.6.2
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) \sqrt {a+b x^4}}{x^3} \, dx\) [502]
3.6.3
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) \sqrt {a+b x^4}}{x^4} \, dx\) [503]
3.6.4
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) \sqrt {a+b x^4}}{x^5} \, dx\) [504]
3.6.5
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) \sqrt {a+b x^4}}{x^6} \, dx\) [505]
3.6.6
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) \sqrt {a+b x^4}}{x^7} \, dx\) [506]
3.6.7
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) \sqrt {a+b x^4}}{x^8} \, dx\) [507]
3.6.8
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) \sqrt {a+b x^4}}{x^9} \, dx\) [508]
3.6.9
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) \sqrt {a+b x^4}}{x^{10}} \, dx\) [509]
3.6.10
\(\int x^4 (c+d x+e x^2+f x^3) (a+b x^4)^{3/2} \, dx\) [510]
3.6.11
\(\int x^3 (c+d x+e x^2+f x^3) (a+b x^4)^{3/2} \, dx\) [511]
3.6.12
\(\int x^2 (c+d x+e x^2+f x^3) (a+b x^4)^{3/2} \, dx\) [512]
3.6.13
\(\int x (c+d x+e x^2+f x^3) (a+b x^4)^{3/2} \, dx\) [513]
3.6.14
\(\int (c+d x+e x^2+f x^3) (a+b x^4)^{3/2} \, dx\) [514]
3.6.15
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x} \, dx\) [515]
3.6.16
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^2} \, dx\) [516]
3.6.17
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^3} \, dx\) [517]
3.6.18
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^4} \, dx\) [518]
3.6.19
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^5} \, dx\) [519]
3.6.20
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^6} \, dx\) [520]
3.6.21
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^7} \, dx\) [521]
3.6.22
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^8} \, dx\) [522]
3.6.23
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^9} \, dx\) [523]
3.6.24
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^{10}} \, dx\) [524]
3.6.25
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^{11}} \, dx\) [525]
3.6.26
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^{12}} \, dx\) [526]
3.6.27
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^{13}} \, dx\) [527]
3.6.28
\(\int \genfrac {}{}{}{}{(c+d x+e x^2+f x^3) (a+b x^4)^{3/2}}{x^{14}} \, dx\) [528]
3.6.29
\(\int \genfrac {}{}{}{}{x^4 (c+d x+e x^2+f x^3)}{\sqrt {a+b x^4}} \, dx\) [529]
3.6.30
\(\int \genfrac {}{}{}{}{x^3 (c+d x+e x^2+f x^3)}{\sqrt {a+b x^4}} \, dx\) [530]
3.6.31
\(\int \genfrac {}{}{}{}{x^2 (c+d x+e x^2+f x^3)}{\sqrt {a+b x^4}} \, dx\) [531]
3.6.32
\(\int \genfrac {}{}{}{}{x (c+d x+e x^2+f x^3)}{\sqrt {a+b x^4}} \, dx\) [532]
3.6.33
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{\sqrt {a+b x^4}} \, dx\) [533]
3.6.34
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x \sqrt {a+b x^4}} \, dx\) [534]
3.6.35
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x^2 \sqrt {a+b x^4}} \, dx\) [535]
3.6.36
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x^3 \sqrt {a+b x^4}} \, dx\) [536]
3.6.37
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x^4 \sqrt {a+b x^4}} \, dx\) [537]
3.6.38
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x^5 \sqrt {a+b x^4}} \, dx\) [538]
3.6.39
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x^6 \sqrt {a+b x^4}} \, dx\) [539]
3.6.40
\(\int \genfrac {}{}{}{}{x^6 (c+d x+e x^2+f x^3)}{(a+b x^4)^{3/2}} \, dx\) [540]
3.6.41
\(\int \genfrac {}{}{}{}{x^5 (c+d x+e x^2+f x^3)}{(a+b x^4)^{3/2}} \, dx\) [541]
3.6.42
\(\int \genfrac {}{}{}{}{x^4 (c+d x+e x^2+f x^3)}{(a+b x^4)^{3/2}} \, dx\) [542]
3.6.43
\(\int \genfrac {}{}{}{}{x^3 (c+d x+e x^2+f x^3)}{(a+b x^4)^{3/2}} \, dx\) [543]
3.6.44
\(\int \genfrac {}{}{}{}{x^2 (c+d x+e x^2+f x^3)}{(a+b x^4)^{3/2}} \, dx\) [544]
3.6.45
\(\int \genfrac {}{}{}{}{x (c+d x+e x^2+f x^3)}{(a+b x^4)^{3/2}} \, dx\) [545]
3.6.46
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{(a+b x^4)^{3/2}} \, dx\) [546]
3.6.47
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x (a+b x^4)^{3/2}} \, dx\) [547]
3.6.48
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x^2 (a+b x^4)^{3/2}} \, dx\) [548]
3.6.49
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x^3 (a+b x^4)^{3/2}} \, dx\) [549]
3.6.50
\(\int \genfrac {}{}{}{}{c+d x+e x^2+f x^3}{x^4 (a+b x^4)^{3/2}} \, dx\) [550]
3.6.51
\(\int (g x)^m (c+d x+e x^2+f x^3) (a+b x^4)^p \, dx\) [551]
3.6.52
\(\int (c+d x+e x^2+f x^3) (a+b x^4)^p \, dx\) [552]
3.6.53
\(\int x^3 (c+d x+e x^2+f x^3) (a+b x^4)^p \, dx\) [553]
3.6.54
\(\int \genfrac {}{}{}{}{1+x+x^2+x^3+x^4}{1-x^5} \, dx\) [554]
3.6.55
\(\int \genfrac {}{}{}{}{243-162 x+108 x^2-72 x^3+48 x^4-32 x^5}{729-64 x^6} \, dx\) [555]
3.6.56
\(\int \genfrac {}{}{}{}{243+162 x+108 x^2+72 x^3+48 x^4+32 x^5}{729-64 x^6} \, dx\) [556]
3.6.57
\(\int \genfrac {}{}{}{}{81+36 x^2+16 x^4}{729-64 x^6} \, dx\) [557]
3.6.58
\(\int \genfrac {}{}{}{}{81+54 x-24 x^3-16 x^4}{729-64 x^6} \, dx\) [558]
3.6.59
\(\int \genfrac {}{}{}{}{3-2 x}{729-64 x^6} \, dx\) [559]
3.6.60
\(\int \genfrac {}{}{}{}{3+2 x}{729-64 x^6} \, dx\) [560]
3.6.61
\(\int \genfrac {}{}{}{}{9-6 x+4 x^2}{729-64 x^6} \, dx\) [561]
3.6.62
\(\int \genfrac {}{}{}{}{9+6 x+4 x^2}{729-64 x^6} \, dx\) [562]
3.6.63
\(\int \genfrac {}{}{}{}{27-8 x^3}{729-64 x^6} \, dx\) [563]
3.6.64
\(\int \genfrac {}{}{}{}{27+36 x+24 x^2+8 x^3}{729-64 x^6} \, dx\) [564]
3.6.65
\(\int \genfrac {}{}{}{}{243-162 x+108 x^2-72 x^3+48 x^4-32 x^5}{(729-64 x^6)^2} \, dx\) [565]
3.6.66
\(\int \genfrac {}{}{}{}{243+162 x+108 x^2+72 x^3+48 x^4+32 x^5}{(729-64 x^6)^2} \, dx\) [566]
3.6.67
\(\int \genfrac {}{}{}{}{81+36 x^2+16 x^4}{(729-64 x^6)^2} \, dx\) [567]
3.6.68
\(\int \genfrac {}{}{}{}{81+54 x-24 x^3-16 x^4}{(729-64 x^6)^2} \, dx\) [568]
3.6.69
\(\int \genfrac {}{}{}{}{3-2 x}{(729-64 x^6)^2} \, dx\) [569]
3.6.70
\(\int \genfrac {}{}{}{}{3+2 x}{(729-64 x^6)^2} \, dx\) [570]
3.6.71
\(\int \genfrac {}{}{}{}{9-6 x+4 x^2}{(729-64 x^6)^2} \, dx\) [571]
3.6.72
\(\int \genfrac {}{}{}{}{9+6 x+4 x^2}{(729-64 x^6)^2} \, dx\) [572]
3.6.73
\(\int \genfrac {}{}{}{}{27-8 x^3}{(729-64 x^6)^2} \, dx\) [573]
3.6.74
\(\int \genfrac {}{}{}{}{27+36 x+24 x^2+8 x^3}{(729-64 x^6)^2} \, dx\) [574]
3.6.75
\(\int \genfrac {}{}{}{}{x (27-2 x^3)}{729-64 x^6} \, dx\) [575]
3.6.76
\(\int \genfrac {}{}{}{}{(c x)^m (d+e x^n+f x^{2 n}+g x^{3 n})}{a+b x^n} \, dx\) [576]
3.6.77
\(\int (c+d x^{-1+n}) (a+b x^n)^3 \, dx\) [577]
3.6.78
\(\int (c+d x^{-1+n}) (a+b x^n)^2 \, dx\) [578]
3.6.79
\(\int (c+d x^{-1+n}) (a+b x^n) \, dx\) [579]
3.6.80
\(\int (c+d x^{-1+n}) \, dx\) [580]
3.6.81
\(\int \genfrac {}{}{}{}{c+d x^{-1+n}}{a+b x^n} \, dx\) [581]
3.6.82
\(\int \genfrac {}{}{}{}{c+d x^{-1+n}}{(a+b x^n)^2} \, dx\) [582]
3.6.83
\(\int \genfrac {}{}{}{}{c+d x^{-1+n}}{(a+b x^n)^3} \, dx\) [583]
3.6.84
\(\int \genfrac {}{}{}{}{(c x)^m (d+e x^n+f x^{2 n}+g x^{3 n})}{\sqrt {a+b x^n}} \, dx\) [584]
3.6.85
\(\int \genfrac {}{}{}{}{-a h x^{-1+\genfrac {}{}{}{}{n}{4}}+b f x^{-1+\genfrac {}{}{}{}{n}{2}}+b g x^{-1+n}+b h x^{-1+\genfrac {}{}{}{}{5 n}{4}}}{(a+b x^n)^{3/2}} \, dx\) [585]
3.6.86
\(\int (c x)^m (d+e x+f x^2+g x^3) (a+b x^n)^p \, dx\) [586]
3.6.87
\(\int (c x)^m (a+b x^n)^p (d+e x^n+f x^{2 n}+g x^{3 n}) \, dx\) [587]
3.6.88
\(\int \genfrac {}{}{}{}{c+d x^{n/2}+e x^n+f x^{3 n/2}}{(a+b x^n)^2} \, dx\) [588]
3.6.89
\(\int \genfrac {}{}{}{}{a c+2 (b c+a d) x^2+3 b d x^4}{\sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [589]
3.6.90
\(\int \genfrac {}{}{}{}{1+x^3}{(1-x^4) \sqrt [4]{1+x^4}} \, dx\) [590]
3.6.91
\(\int (a+b x^n)^{\genfrac {}{}{}{}{-1-n}{n}} (c+d x^n)^{\genfrac {}{}{}{}{-1-n}{n}} (a c-b d x^{2 n}) \, dx\) [591]
3.6.92
\(\int (h x)^{-1-n-n p} (a+b x^n)^p (c+d x^n)^p (a c-b d x^{2 n}) \, dx\) [592]
3.6.93
\(\int (a+b x^n)^p (c+d x^n)^p (e+\genfrac {}{}{}{}{(b c+a d) e (1+n+n p) x^n}{a c}+\genfrac {}{}{}{}{b d e (1+2 n+2 n p) x^{2 n}}{a c}) \, dx\) [593]
3.6.94
\(\int (h x)^m (a+b x^n)^p (c+d x^n)^p (e+\genfrac {}{}{}{}{(b c+a d) e (1+m+n+n p) x^n}{a c (1+m)}+\genfrac {}{}{}{}{b d e (1+m+2 n+2 n p) x^{2 n}}{a c (1+m)}) \, dx\) [594]
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