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3.9
Integrals 801 to 900
3.9.1
\(\int \genfrac {}{}{}{}{\sqrt {c+a^2 c x^2} \text {ArcTan}(a x)^{3/2}}{x} \, dx\) [801]
3.9.2
\(\int x^m (c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{3/2} \, dx\) [802]
3.9.3
\(\int x^2 (c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{3/2} \, dx\) [803]
3.9.4
\(\int x (c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{3/2} \, dx\) [804]
3.9.5
\(\int (c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{3/2} \, dx\) [805]
3.9.6
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{3/2}}{x} \, dx\) [806]
3.9.7
\(\int x^m (c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{3/2} \, dx\) [807]
3.9.8
\(\int x^2 (c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{3/2} \, dx\) [808]
3.9.9
\(\int x (c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{3/2} \, dx\) [809]
3.9.10
\(\int (c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{3/2} \, dx\) [810]
3.9.11
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{3/2}}{x} \, dx\) [811]
3.9.12
\(\int \genfrac {}{}{}{}{x^m \text {ArcTan}(a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [812]
3.9.13
\(\int \genfrac {}{}{}{}{x^3 \text {ArcTan}(a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [813]
3.9.14
\(\int \genfrac {}{}{}{}{x^2 \text {ArcTan}(a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [814]
3.9.15
\(\int \genfrac {}{}{}{}{x \text {ArcTan}(a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [815]
3.9.16
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [816]
3.9.17
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{x \sqrt {c+a^2 c x^2}} \, dx\) [817]
3.9.18
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{x^2 \sqrt {c+a^2 c x^2}} \, dx\) [818]
3.9.19
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{x^3 \sqrt {c+a^2 c x^2}} \, dx\) [819]
3.9.20
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{x^4 \sqrt {c+a^2 c x^2}} \, dx\) [820]
3.9.21
\(\int \genfrac {}{}{}{}{x^m \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [821]
3.9.22
\(\int \genfrac {}{}{}{}{x^3 \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [822]
3.9.23
\(\int \genfrac {}{}{}{}{x^2 \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [823]
3.9.24
\(\int \genfrac {}{}{}{}{x \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [824]
3.9.25
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [825]
3.9.26
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{x (c+a^2 c x^2)^{3/2}} \, dx\) [826]
3.9.27
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{x^2 (c+a^2 c x^2)^{3/2}} \, dx\) [827]
3.9.28
\(\int \genfrac {}{}{}{}{x^m \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [828]
3.9.29
\(\int \genfrac {}{}{}{}{x^5 \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [829]
3.9.30
\(\int \genfrac {}{}{}{}{x^4 \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [830]
3.9.31
\(\int \genfrac {}{}{}{}{x^3 \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [831]
3.9.32
\(\int \genfrac {}{}{}{}{x^2 \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [832]
3.9.33
\(\int \genfrac {}{}{}{}{x \text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [833]
3.9.34
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [834]
3.9.35
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{x (c+a^2 c x^2)^{5/2}} \, dx\) [835]
3.9.36
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{3/2}}{x^2 (c+a^2 c x^2)^{5/2}} \, dx\) [836]
3.9.37
\(\int x^m (c+a^2 c x^2) \text {ArcTan}(a x)^{5/2} \, dx\) [837]
3.9.38
\(\int x^2 (c+a^2 c x^2) \text {ArcTan}(a x)^{5/2} \, dx\) [838]
3.9.39
\(\int x (c+a^2 c x^2) \text {ArcTan}(a x)^{5/2} \, dx\) [839]
3.9.40
\(\int (c+a^2 c x^2) \text {ArcTan}(a x)^{5/2} \, dx\) [840]
3.9.41
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2) \text {ArcTan}(a x)^{5/2}}{x} \, dx\) [841]
3.9.42
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2) \text {ArcTan}(a x)^{5/2}}{x^2} \, dx\) [842]
3.9.43
\(\int x^m (c+a^2 c x^2)^2 \text {ArcTan}(a x)^{5/2} \, dx\) [843]
3.9.44
\(\int x^2 (c+a^2 c x^2)^2 \text {ArcTan}(a x)^{5/2} \, dx\) [844]
3.9.45
\(\int x (c+a^2 c x^2)^2 \text {ArcTan}(a x)^{5/2} \, dx\) [845]
3.9.46
\(\int (c+a^2 c x^2)^2 \text {ArcTan}(a x)^{5/2} \, dx\) [846]
3.9.47
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^2 \text {ArcTan}(a x)^{5/2}}{x} \, dx\) [847]
3.9.48
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^2 \text {ArcTan}(a x)^{5/2}}{x^2} \, dx\) [848]
3.9.49
\(\int x^m (c+a^2 c x^2)^3 \text {ArcTan}(a x)^{5/2} \, dx\) [849]
3.9.50
\(\int x^2 (c+a^2 c x^2)^3 \text {ArcTan}(a x)^{5/2} \, dx\) [850]
3.9.51
\(\int x (c+a^2 c x^2)^3 \text {ArcTan}(a x)^{5/2} \, dx\) [851]
3.9.52
\(\int (c+a^2 c x^2)^3 \text {ArcTan}(a x)^{5/2} \, dx\) [852]
3.9.53
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^3 \text {ArcTan}(a x)^{5/2}}{x} \, dx\) [853]
3.9.54
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^3 \text {ArcTan}(a x)^{5/2}}{x^2} \, dx\) [854]
3.9.55
\(\int \genfrac {}{}{}{}{x^m \text {ArcTan}(a x)^{5/2}}{c+a^2 c x^2} \, dx\) [855]
3.9.56
\(\int \genfrac {}{}{}{}{x^3 \text {ArcTan}(a x)^{5/2}}{c+a^2 c x^2} \, dx\) [856]
3.9.57
\(\int \genfrac {}{}{}{}{x^2 \text {ArcTan}(a x)^{5/2}}{c+a^2 c x^2} \, dx\) [857]
3.9.58
\(\int \genfrac {}{}{}{}{x \text {ArcTan}(a x)^{5/2}}{c+a^2 c x^2} \, dx\) [858]
3.9.59
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{c+a^2 c x^2} \, dx\) [859]
3.9.60
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{x (c+a^2 c x^2)} \, dx\) [860]
3.9.61
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{x^2 (c+a^2 c x^2)} \, dx\) [861]
3.9.62
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{x^3 (c+a^2 c x^2)} \, dx\) [862]
3.9.63
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{x^4 (c+a^2 c x^2)} \, dx\) [863]
3.9.64
\(\int \genfrac {}{}{}{}{x^m \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [864]
3.9.65
\(\int \genfrac {}{}{}{}{x^3 \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [865]
3.9.66
\(\int \genfrac {}{}{}{}{x^2 \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [866]
3.9.67
\(\int \genfrac {}{}{}{}{x \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [867]
3.9.68
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [868]
3.9.69
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{x (c+a^2 c x^2)^2} \, dx\) [869]
3.9.70
\(\int \genfrac {}{}{}{}{x^m \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [870]
3.9.71
\(\int \genfrac {}{}{}{}{x^5 \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [871]
3.9.72
\(\int \genfrac {}{}{}{}{x^4 \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [872]
3.9.73
\(\int \genfrac {}{}{}{}{x^3 \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [873]
3.9.74
\(\int \genfrac {}{}{}{}{x^2 \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [874]
3.9.75
\(\int \genfrac {}{}{}{}{x \text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [875]
3.9.76
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [876]
3.9.77
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{x (c+a^2 c x^2)^3} \, dx\) [877]
3.9.78
\(\int x^m \sqrt {c+a^2 c x^2} \text {ArcTan}(a x)^{5/2} \, dx\) [878]
3.9.79
\(\int x^2 \sqrt {c+a^2 c x^2} \text {ArcTan}(a x)^{5/2} \, dx\) [879]
3.9.80
\(\int x \sqrt {c+a^2 c x^2} \text {ArcTan}(a x)^{5/2} \, dx\) [880]
3.9.81
\(\int \sqrt {c+a^2 c x^2} \text {ArcTan}(a x)^{5/2} \, dx\) [881]
3.9.82
\(\int \genfrac {}{}{}{}{\sqrt {c+a^2 c x^2} \text {ArcTan}(a x)^{5/2}}{x} \, dx\) [882]
3.9.83
\(\int x^m (c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{5/2} \, dx\) [883]
3.9.84
\(\int x^2 (c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{5/2} \, dx\) [884]
3.9.85
\(\int x (c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{5/2} \, dx\) [885]
3.9.86
\(\int (c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{5/2} \, dx\) [886]
3.9.87
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{3/2} \text {ArcTan}(a x)^{5/2}}{x} \, dx\) [887]
3.9.88
\(\int x^m (c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{5/2} \, dx\) [888]
3.9.89
\(\int x^2 (c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{5/2} \, dx\) [889]
3.9.90
\(\int x (c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{5/2} \, dx\) [890]
3.9.91
\(\int (c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{5/2} \, dx\) [891]
3.9.92
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{5/2} \text {ArcTan}(a x)^{5/2}}{x} \, dx\) [892]
3.9.93
\(\int \genfrac {}{}{}{}{x^m \text {ArcTan}(a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [893]
3.9.94
\(\int \genfrac {}{}{}{}{x^3 \text {ArcTan}(a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [894]
3.9.95
\(\int \genfrac {}{}{}{}{x^2 \text {ArcTan}(a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [895]
3.9.96
\(\int \genfrac {}{}{}{}{x \text {ArcTan}(a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [896]
3.9.97
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [897]
3.9.98
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{x \sqrt {c+a^2 c x^2}} \, dx\) [898]
3.9.99
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{x^2 \sqrt {c+a^2 c x^2}} \, dx\) [899]
3.9.100
\(\int \genfrac {}{}{}{}{\text {ArcTan}(a x)^{5/2}}{x^3 \sqrt {c+a^2 c x^2}} \, dx\) [900]
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