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