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3.7
Integrals 601 to 700
3.7.1
\(\int \genfrac {}{}{}{}{(a+b x^2)^{3/2}}{\sqrt {c x}} \, dx\) [601]
3.7.2
\(\int \genfrac {}{}{}{}{(a+b x^2)^{3/2}}{(c x)^{3/2}} \, dx\) [602]
3.7.3
\(\int \genfrac {}{}{}{}{(a+b x^2)^{3/2}}{(c x)^{5/2}} \, dx\) [603]
3.7.4
\(\int \genfrac {}{}{}{}{(a+b x^2)^{3/2}}{(c x)^{7/2}} \, dx\) [604]
3.7.5
\(\int \genfrac {}{}{}{}{(a+b x^2)^{3/2}}{(c x)^{9/2}} \, dx\) [605]
3.7.6
\(\int \genfrac {}{}{}{}{(a+b x^2)^{3/2}}{(c x)^{11/2}} \, dx\) [606]
3.7.7
\(\int (c x)^{5/2} \sqrt {3 a-2 a x^2} \, dx\) [607]
3.7.8
\(\int (c x)^{3/2} \sqrt {3 a-2 a x^2} \, dx\) [608]
3.7.9
\(\int \sqrt {c x} \sqrt {3 a-2 a x^2} \, dx\) [609]
3.7.10
\(\int \genfrac {}{}{}{}{\sqrt {3 a-2 a x^2}}{\sqrt {c x}} \, dx\) [610]
3.7.11
\(\int \genfrac {}{}{}{}{\sqrt {3 a-2 a x^2}}{(c x)^{3/2}} \, dx\) [611]
3.7.12
\(\int \genfrac {}{}{}{}{\sqrt {3 a-2 a x^2}}{(c x)^{5/2}} \, dx\) [612]
3.7.13
\(\int \genfrac {}{}{}{}{(c x)^{7/2}}{\sqrt {a+b x^2}} \, dx\) [613]
3.7.14
\(\int \genfrac {}{}{}{}{(c x)^{5/2}}{\sqrt {a+b x^2}} \, dx\) [614]
3.7.15
\(\int \genfrac {}{}{}{}{(c x)^{3/2}}{\sqrt {a+b x^2}} \, dx\) [615]
3.7.16
\(\int \genfrac {}{}{}{}{\sqrt {c x}}{\sqrt {a+b x^2}} \, dx\) [616]
3.7.17
\(\int \genfrac {}{}{}{}{1}{\sqrt {c x} \sqrt {a+b x^2}} \, dx\) [617]
3.7.18
\(\int \genfrac {}{}{}{}{1}{(c x)^{3/2} \sqrt {a+b x^2}} \, dx\) [618]
3.7.19
\(\int \genfrac {}{}{}{}{1}{(c x)^{5/2} \sqrt {a+b x^2}} \, dx\) [619]
3.7.20
\(\int \genfrac {}{}{}{}{1}{(c x)^{7/2} \sqrt {a+b x^2}} \, dx\) [620]
3.7.21
\(\int \genfrac {}{}{}{}{(c x)^{7/2}}{(a+b x^2)^{3/2}} \, dx\) [621]
3.7.22
\(\int \genfrac {}{}{}{}{(c x)^{5/2}}{(a+b x^2)^{3/2}} \, dx\) [622]
3.7.23
\(\int \genfrac {}{}{}{}{(c x)^{3/2}}{(a+b x^2)^{3/2}} \, dx\) [623]
3.7.24
\(\int \genfrac {}{}{}{}{\sqrt {c x}}{(a+b x^2)^{3/2}} \, dx\) [624]
3.7.25
\(\int \genfrac {}{}{}{}{1}{\sqrt {c x} (a+b x^2)^{3/2}} \, dx\) [625]
3.7.26
\(\int \genfrac {}{}{}{}{1}{(c x)^{3/2} (a+b x^2)^{3/2}} \, dx\) [626]
3.7.27
\(\int \genfrac {}{}{}{}{1}{(c x)^{5/2} (a+b x^2)^{3/2}} \, dx\) [627]
3.7.28
\(\int \genfrac {}{}{}{}{1}{(c x)^{7/2} (a+b x^2)^{3/2}} \, dx\) [628]
3.7.29
\(\int \genfrac {}{}{}{}{(c x)^{7/2}}{(a+b x^2)^{5/2}} \, dx\) [629]
3.7.30
\(\int \genfrac {}{}{}{}{(c x)^{5/2}}{(a+b x^2)^{5/2}} \, dx\) [630]
3.7.31
\(\int \genfrac {}{}{}{}{(c x)^{3/2}}{(a+b x^2)^{5/2}} \, dx\) [631]
3.7.32
\(\int \genfrac {}{}{}{}{\sqrt {c x}}{(a+b x^2)^{5/2}} \, dx\) [632]
3.7.33
\(\int \genfrac {}{}{}{}{1}{\sqrt {c x} (a+b x^2)^{5/2}} \, dx\) [633]
3.7.34
\(\int \genfrac {}{}{}{}{1}{(c x)^{3/2} (a+b x^2)^{5/2}} \, dx\) [634]
3.7.35
\(\int \genfrac {}{}{}{}{1}{(c x)^{5/2} (a+b x^2)^{5/2}} \, dx\) [635]
3.7.36
\(\int \genfrac {}{}{}{}{1}{(c x)^{7/2} (a+b x^2)^{5/2}} \, dx\) [636]
3.7.37
\(\int \genfrac {}{}{}{}{(c x)^{5/2}}{\sqrt {3 a-2 a x^2}} \, dx\) [637]
3.7.38
\(\int \genfrac {}{}{}{}{(c x)^{3/2}}{\sqrt {3 a-2 a x^2}} \, dx\) [638]
3.7.39
\(\int \genfrac {}{}{}{}{\sqrt {c x}}{\sqrt {3 a-2 a x^2}} \, dx\) [639]
3.7.40
\(\int \genfrac {}{}{}{}{1}{\sqrt {c x} \sqrt {3 a-2 a x^2}} \, dx\) [640]
3.7.41
\(\int \genfrac {}{}{}{}{1}{(c x)^{3/2} \sqrt {3 a-2 a x^2}} \, dx\) [641]
3.7.42
\(\int \genfrac {}{}{}{}{1}{(c x)^{5/2} \sqrt {3 a-2 a x^2}} \, dx\) [642]
3.7.43
\(\int \genfrac {}{}{}{}{(c x)^{5/2}}{(3 a-2 a x^2)^{3/2}} \, dx\) [643]
3.7.44
\(\int \genfrac {}{}{}{}{(c x)^{3/2}}{(3 a-2 a x^2)^{3/2}} \, dx\) [644]
3.7.45
\(\int \genfrac {}{}{}{}{\sqrt {c x}}{(3 a-2 a x^2)^{3/2}} \, dx\) [645]
3.7.46
\(\int \genfrac {}{}{}{}{1}{\sqrt {c x} (3 a-2 a x^2)^{3/2}} \, dx\) [646]
3.7.47
\(\int \genfrac {}{}{}{}{1}{(c x)^{3/2} (3 a-2 a x^2)^{3/2}} \, dx\) [647]
3.7.48
\(\int \genfrac {}{}{}{}{1}{(c x)^{5/2} (3 a-2 a x^2)^{3/2}} \, dx\) [648]
3.7.49
\(\int \genfrac {}{}{}{}{1}{\sqrt {x} \sqrt {1-a^2 x^2}} \, dx\) [649]
3.7.50
\(\int \genfrac {}{}{}{}{1}{\sqrt {x} \sqrt {1+a x^2}} \, dx\) [650]
3.7.51
\(\int x^m (a+b x^2)^{3/2} \, dx\) [651]
3.7.52
\(\int x^m \sqrt {a+b x^2} \, dx\) [652]
3.7.53
\(\int \genfrac {}{}{}{}{x^m}{\sqrt {a+b x^2}} \, dx\) [653]
3.7.54
\(\int \genfrac {}{}{}{}{x^m}{(a+b x^2)^{3/2}} \, dx\) [654]
3.7.55
\(\int \genfrac {}{}{}{}{x^m}{(a+b x^2)^{5/2}} \, dx\) [655]
3.7.56
\(\int \genfrac {}{}{}{}{x^{2+m}}{\sqrt {a+b x^2}} \, dx\) [656]
3.7.57
\(\int \genfrac {}{}{}{}{x^{1+m}}{\sqrt {a+b x^2}} \, dx\) [657]
3.7.58
\(\int \genfrac {}{}{}{}{x^m}{\sqrt {a+b x^2}} \, dx\) [658]
3.7.59
\(\int \genfrac {}{}{}{}{x^{-1+m}}{\sqrt {a+b x^2}} \, dx\) [659]
3.7.60
\(\int \genfrac {}{}{}{}{x^{-2+m}}{\sqrt {a+b x^2}} \, dx\) [660]
3.7.61
\(\int \genfrac {}{}{}{}{x^{1+m} (a (2+m)+b (3+m) x^2)}{\sqrt {a+b x^2}} \, dx\) [661]
3.7.62
\(\int (\genfrac {}{}{}{}{a (2+m) x^{1+m}}{\sqrt {a+b x^2}}+\genfrac {}{}{}{}{b (3+m) x^{3+m}}{\sqrt {a+b x^2}}) \, dx\) [662]
3.7.63
\(\int \genfrac {}{}{}{}{x^{-1+m} (a m+b (-1+m) x^2)}{(a+b x^2)^{3/2}} \, dx\) [663]
3.7.64
\(\int (-\genfrac {}{}{}{}{b x^{1+m}}{(a+b x^2)^{3/2}}+\genfrac {}{}{}{}{m x^{-1+m}}{\sqrt {a+b x^2}}) \, dx\) [664]
3.7.65
\(\int x^7 \sqrt [3]{a+b x^2} \, dx\) [665]
3.7.66
\(\int x^5 \sqrt [3]{a+b x^2} \, dx\) [666]
3.7.67
\(\int x^3 \sqrt [3]{a+b x^2} \, dx\) [667]
3.7.68
\(\int x \sqrt [3]{a+b x^2} \, dx\) [668]
3.7.69
\(\int \genfrac {}{}{}{}{\sqrt [3]{a+b x^2}}{x} \, dx\) [669]
3.7.70
\(\int \genfrac {}{}{}{}{\sqrt [3]{a+b x^2}}{x^3} \, dx\) [670]
3.7.71
\(\int \genfrac {}{}{}{}{\sqrt [3]{a+b x^2}}{x^5} \, dx\) [671]
3.7.72
\(\int x^4 \sqrt [3]{a+b x^2} \, dx\) [672]
3.7.73
\(\int x^2 \sqrt [3]{a+b x^2} \, dx\) [673]
3.7.74
\(\int \sqrt [3]{a+b x^2} \, dx\) [674]
3.7.75
\(\int \genfrac {}{}{}{}{\sqrt [3]{a+b x^2}}{x^2} \, dx\) [675]
3.7.76
\(\int \genfrac {}{}{}{}{\sqrt [3]{a+b x^2}}{x^4} \, dx\) [676]
3.7.77
\(\int x^7 (a+b x^2)^{2/3} \, dx\) [677]
3.7.78
\(\int x^5 (a+b x^2)^{2/3} \, dx\) [678]
3.7.79
\(\int x^3 (a+b x^2)^{2/3} \, dx\) [679]
3.7.80
\(\int x (a+b x^2)^{2/3} \, dx\) [680]
3.7.81
\(\int \genfrac {}{}{}{}{(a+b x^2)^{2/3}}{x} \, dx\) [681]
3.7.82
\(\int \genfrac {}{}{}{}{(a+b x^2)^{2/3}}{x^3} \, dx\) [682]
3.7.83
\(\int \genfrac {}{}{}{}{(a+b x^2)^{2/3}}{x^5} \, dx\) [683]
3.7.84
\(\int x^4 (a+b x^2)^{2/3} \, dx\) [684]
3.7.85
\(\int x^2 (a+b x^2)^{2/3} \, dx\) [685]
3.7.86
\(\int (a+b x^2)^{2/3} \, dx\) [686]
3.7.87
\(\int \genfrac {}{}{}{}{(a+b x^2)^{2/3}}{x^2} \, dx\) [687]
3.7.88
\(\int \genfrac {}{}{}{}{(a+b x^2)^{2/3}}{x^4} \, dx\) [688]
3.7.89
\(\int x^7 (a+b x^2)^{4/3} \, dx\) [689]
3.7.90
\(\int x^5 (a+b x^2)^{4/3} \, dx\) [690]
3.7.91
\(\int x^3 (a+b x^2)^{4/3} \, dx\) [691]
3.7.92
\(\int x (a+b x^2)^{4/3} \, dx\) [692]
3.7.93
\(\int \genfrac {}{}{}{}{(a+b x^2)^{4/3}}{x} \, dx\) [693]
3.7.94
\(\int \genfrac {}{}{}{}{(a+b x^2)^{4/3}}{x^3} \, dx\) [694]
3.7.95
\(\int \genfrac {}{}{}{}{(a+b x^2)^{4/3}}{x^5} \, dx\) [695]
3.7.96
\(\int x^4 (a+b x^2)^{4/3} \, dx\) [696]
3.7.97
\(\int x^2 (a+b x^2)^{4/3} \, dx\) [697]
3.7.98
\(\int (a+b x^2)^{4/3} \, dx\) [698]
3.7.99
\(\int \genfrac {}{}{}{}{(a+b x^2)^{4/3}}{x^2} \, dx\) [699]
3.7.100
\(\int \genfrac {}{}{}{}{(a+b x^2)^{4/3}}{x^4} \, dx\) [700]
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