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3.5
Integrals 401 to 500
3.5.1
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^2}{x^2 (1-a^2 x^2)^{3/2}} \, dx\) [401]
3.5.2
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^2}{x^3 (1-a^2 x^2)^{3/2}} \, dx\) [402]
3.5.3
\(\int \genfrac {}{}{}{}{x^m \text {arctanh}(a x)^3}{(1-a^2 x^2)^{3/2}} \, dx\) [403]
3.5.4
\(\int \genfrac {}{}{}{}{x^3 \text {arctanh}(a x)^3}{(1-a^2 x^2)^{3/2}} \, dx\) [404]
3.5.5
\(\int \genfrac {}{}{}{}{x^2 \text {arctanh}(a x)^3}{(1-a^2 x^2)^{3/2}} \, dx\) [405]
3.5.6
\(\int \genfrac {}{}{}{}{x \text {arctanh}(a x)^3}{(1-a^2 x^2)^{3/2}} \, dx\) [406]
3.5.7
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^3}{(1-a^2 x^2)^{3/2}} \, dx\) [407]
3.5.8
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^3}{x (1-a^2 x^2)^{3/2}} \, dx\) [408]
3.5.9
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^3}{x^2 (1-a^2 x^2)^{3/2}} \, dx\) [409]
3.5.10
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^3}{x^3 (1-a^2 x^2)^{3/2}} \, dx\) [410]
3.5.11
\(\int \genfrac {}{}{}{}{x^m}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)} \, dx\) [411]
3.5.12
\(\int \genfrac {}{}{}{}{x^2}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)} \, dx\) [412]
3.5.13
\(\int \genfrac {}{}{}{}{x}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)} \, dx\) [413]
3.5.14
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)} \, dx\) [414]
3.5.15
\(\int \genfrac {}{}{}{}{1}{x (1-a^2 x^2)^{3/2} \text {arctanh}(a x)} \, dx\) [415]
3.5.16
\(\int \genfrac {}{}{}{}{x^m}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^2} \, dx\) [416]
3.5.17
\(\int \genfrac {}{}{}{}{x^2}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^2} \, dx\) [417]
3.5.18
\(\int \genfrac {}{}{}{}{x}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^2} \, dx\) [418]
3.5.19
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^2} \, dx\) [419]
3.5.20
\(\int \genfrac {}{}{}{}{1}{x (1-a^2 x^2)^{3/2} \text {arctanh}(a x)^2} \, dx\) [420]
3.5.21
\(\int \genfrac {}{}{}{}{x^m}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^3} \, dx\) [421]
3.5.22
\(\int \genfrac {}{}{}{}{x^2}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^3} \, dx\) [422]
3.5.23
\(\int \genfrac {}{}{}{}{x}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^3} \, dx\) [423]
3.5.24
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^3} \, dx\) [424]
3.5.25
\(\int \genfrac {}{}{}{}{1}{x (1-a^2 x^2)^{3/2} \text {arctanh}(a x)^3} \, dx\) [425]
3.5.26
\(\int x^4 \sqrt {1-a^2 x^2} \text {arctanh}(a x) \, dx\) [426]
3.5.27
\(\int x^3 \sqrt {1-a^2 x^2} \text {arctanh}(a x) \, dx\) [427]
3.5.28
\(\int x^2 \sqrt {1-a^2 x^2} \text {arctanh}(a x) \, dx\) [428]
3.5.29
\(\int x \sqrt {1-a^2 x^2} \text {arctanh}(a x) \, dx\) [429]
3.5.30
\(\int \sqrt {1-a^2 x^2} \text {arctanh}(a x) \, dx\) [430]
3.5.31
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)}{x} \, dx\) [431]
3.5.32
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)}{x^2} \, dx\) [432]
3.5.33
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)}{x^3} \, dx\) [433]
3.5.34
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)}{x^4} \, dx\) [434]
3.5.35
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)}{x^5} \, dx\) [435]
3.5.36
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)}{x^6} \, dx\) [436]
3.5.37
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)}{x^7} \, dx\) [437]
3.5.38
\(\int x^4 \sqrt {1-a^2 x^2} \text {arctanh}(a x)^2 \, dx\) [438]
3.5.39
\(\int x^3 \sqrt {1-a^2 x^2} \text {arctanh}(a x)^2 \, dx\) [439]
3.5.40
\(\int x^2 \sqrt {1-a^2 x^2} \text {arctanh}(a x)^2 \, dx\) [440]
3.5.41
\(\int x \sqrt {1-a^2 x^2} \text {arctanh}(a x)^2 \, dx\) [441]
3.5.42
\(\int \sqrt {1-a^2 x^2} \text {arctanh}(a x)^2 \, dx\) [442]
3.5.43
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)^2}{x} \, dx\) [443]
3.5.44
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)^2}{x^2} \, dx\) [444]
3.5.45
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)^2}{x^3} \, dx\) [445]
3.5.46
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)^2}{x^4} \, dx\) [446]
3.5.47
\(\int x^4 (1-a^2 x^2)^{3/2} \text {arctanh}(a x) \, dx\) [447]
3.5.48
\(\int x^3 (1-a^2 x^2)^{3/2} \text {arctanh}(a x) \, dx\) [448]
3.5.49
\(\int x^2 (1-a^2 x^2)^{3/2} \text {arctanh}(a x) \, dx\) [449]
3.5.50
\(\int x (1-a^2 x^2)^{3/2} \text {arctanh}(a x) \, dx\) [450]
3.5.51
\(\int (1-a^2 x^2)^{3/2} \text {arctanh}(a x) \, dx\) [451]
3.5.52
\(\int \genfrac {}{}{}{}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)}{x} \, dx\) [452]
3.5.53
\(\int \genfrac {}{}{}{}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)}{x^2} \, dx\) [453]
3.5.54
\(\int \genfrac {}{}{}{}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)}{x^3} \, dx\) [454]
3.5.55
\(\int \genfrac {}{}{}{}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)}{x^4} \, dx\) [455]
3.5.56
\(\int \genfrac {}{}{}{}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)}{x^5} \, dx\) [456]
3.5.57
\(\int \genfrac {}{}{}{}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)}{x^6} \, dx\) [457]
3.5.58
\(\int \genfrac {}{}{}{}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)}{x^7} \, dx\) [458]
3.5.59
\(\int (1-a^2 x^2)^{5/2} \text {arctanh}(a x) \, dx\) [459]
3.5.60
\(\int (1-a^2 x^2)^{3/2} \text {arctanh}(a x) \, dx\) [460]
3.5.61
\(\int \sqrt {1-a^2 x^2} \text {arctanh}(a x) \, dx\) [461]
3.5.62
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)}{(1-a^2 x^2)^{5/2}} \, dx\) [462]
3.5.63
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)}{(1-a^2 x^2)^{7/2}} \, dx\) [463]
3.5.64
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)}{(1-a^2 x^2)^{9/2}} \, dx\) [464]
3.5.65
\(\int (c-a^2 c x^2)^{3/2} \text {arctanh}(a x) \, dx\) [465]
3.5.66
\(\int \sqrt {c-a^2 c x^2} \text {arctanh}(a x) \, dx\) [466]
3.5.67
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)}{\sqrt {c-a^2 c x^2}} \, dx\) [467]
3.5.68
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)}{(c-a^2 c x^2)^{3/2}} \, dx\) [468]
3.5.69
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)}{(c-a^2 c x^2)^{5/2}} \, dx\) [469]
3.5.70
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)}{(c-a^2 c x^2)^{7/2}} \, dx\) [470]
3.5.71
\(\int \sqrt {1-a^2 x^2} \text {arctanh}(a x)^2 \, dx\) [471]
3.5.72
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^2}{(1-a^2 x^2)^{5/2}} \, dx\) [472]
3.5.73
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^2}{(1-a^2 x^2)^{7/2}} \, dx\) [473]
3.5.74
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^2}{(1-a^2 x^2)^{9/2}} \, dx\) [474]
3.5.75
\(\int \sqrt {1-a^2 x^2} \text {arctanh}(a x)^3 \, dx\) [475]
3.5.76
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^3}{(1-a^2 x^2)^{5/2}} \, dx\) [476]
3.5.77
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^3}{(1-a^2 x^2)^{7/2}} \, dx\) [477]
3.5.78
\(\int \genfrac {}{}{}{}{\text {arctanh}(a x)^3}{(1-a^2 x^2)^{9/2}} \, dx\) [478]
3.5.79
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2}}{\text {arctanh}(a x)} \, dx\) [479]
3.5.80
\(\int \genfrac {}{}{}{}{1}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)} \, dx\) [480]
3.5.81
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)} \, dx\) [481]
3.5.82
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{5/2} \text {arctanh}(a x)} \, dx\) [482]
3.5.83
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{7/2} \text {arctanh}(a x)} \, dx\) [483]
3.5.84
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{9/2} \text {arctanh}(a x)} \, dx\) [484]
3.5.85
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2}}{\text {arctanh}(a x)^2} \, dx\) [485]
3.5.86
\(\int \genfrac {}{}{}{}{1}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)^2} \, dx\) [486]
3.5.87
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^2} \, dx\) [487]
3.5.88
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{5/2} \text {arctanh}(a x)^2} \, dx\) [488]
3.5.89
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{7/2} \text {arctanh}(a x)^2} \, dx\) [489]
3.5.90
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{9/2} \text {arctanh}(a x)^2} \, dx\) [490]
3.5.91
\(\int \genfrac {}{}{}{}{\sqrt {1-a^2 x^2}}{\text {arctanh}(a x)^3} \, dx\) [491]
3.5.92
\(\int \genfrac {}{}{}{}{1}{\sqrt {1-a^2 x^2} \text {arctanh}(a x)^3} \, dx\) [492]
3.5.93
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{3/2} \text {arctanh}(a x)^3} \, dx\) [493]
3.5.94
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{5/2} \text {arctanh}(a x)^3} \, dx\) [494]
3.5.95
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{7/2} \text {arctanh}(a x)^3} \, dx\) [495]
3.5.96
\(\int \genfrac {}{}{}{}{1}{(1-a^2 x^2)^{9/2} \text {arctanh}(a x)^3} \, dx\) [496]
3.5.97
\(\int \genfrac {}{}{}{}{(d+e x) (a+b \text {arctanh}(c x))^2}{1-c^2 x^2} \, dx\) [497]
3.5.98
\(\int (c+d x^2)^4 \text {arctanh}(a x) \, dx\) [498]
3.5.99
\(\int (c+d x^2)^3 \text {arctanh}(a x) \, dx\) [499]
3.5.100
\(\int (c+d x^2)^2 \text {arctanh}(a x) \, dx\) [500]
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