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3.4
Integrals 301 to 400
3.4.1
\(\int \genfrac {}{}{}{}{x^4 (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{3/2}} \, dx\) [301]
3.4.2
\(\int \genfrac {}{}{}{}{x^3 (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{3/2}} \, dx\) [302]
3.4.3
\(\int \genfrac {}{}{}{}{x^2 (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{3/2}} \, dx\) [303]
3.4.4
\(\int \genfrac {}{}{}{}{x (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{3/2}} \, dx\) [304]
3.4.5
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{3/2}} \, dx\) [305]
3.4.6
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{x (d+c^2 d x^2)^{3/2}} \, dx\) [306]
3.4.7
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{x^2 (d+c^2 d x^2)^{3/2}} \, dx\) [307]
3.4.8
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{x^3 (d+c^2 d x^2)^{3/2}} \, dx\) [308]
3.4.9
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{x^4 (d+c^2 d x^2)^{3/2}} \, dx\) [309]
3.4.10
\(\int \genfrac {}{}{}{}{x^5 (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{5/2}} \, dx\) [310]
3.4.11
\(\int \genfrac {}{}{}{}{x^4 (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{5/2}} \, dx\) [311]
3.4.12
\(\int \genfrac {}{}{}{}{x^3 (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{5/2}} \, dx\) [312]
3.4.13
\(\int \genfrac {}{}{}{}{x^2 (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{5/2}} \, dx\) [313]
3.4.14
\(\int \genfrac {}{}{}{}{x (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{5/2}} \, dx\) [314]
3.4.15
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{5/2}} \, dx\) [315]
3.4.16
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{x (d+c^2 d x^2)^{5/2}} \, dx\) [316]
3.4.17
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{x^2 (d+c^2 d x^2)^{5/2}} \, dx\) [317]
3.4.18
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{x^3 (d+c^2 d x^2)^{5/2}} \, dx\) [318]
3.4.19
\(\int \genfrac {}{}{}{}{(a+b \text {arcsinh}(c x))^2}{x^4 (d+c^2 d x^2)^{5/2}} \, dx\) [319]
3.4.20
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^2}{(c+a^2 c x^2)^{7/2}} \, dx\) [320]
3.4.21
\(\int x^m (d+c^2 d x^2)^{5/2} (a+b \text {arcsinh}(c x))^2 \, dx\) [321]
3.4.22
\(\int x^m (d+c^2 d x^2)^{3/2} (a+b \text {arcsinh}(c x))^2 \, dx\) [322]
3.4.23
\(\int x^m \sqrt {d+c^2 d x^2} (a+b \text {arcsinh}(c x))^2 \, dx\) [323]
3.4.24
\(\int \genfrac {}{}{}{}{x^m (a+b \text {arcsinh}(c x))^2}{\sqrt {d+c^2 d x^2}} \, dx\) [324]
3.4.25
\(\int \genfrac {}{}{}{}{x^m (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{3/2}} \, dx\) [325]
3.4.26
\(\int \genfrac {}{}{}{}{x^m (a+b \text {arcsinh}(c x))^2}{(d+c^2 d x^2)^{5/2}} \, dx\) [326]
3.4.27
\(\int \genfrac {}{}{}{}{x^m \text {arcsinh}(a x)^2}{\sqrt {1+a^2 x^2}} \, dx\) [327]
3.4.28
\(\int (c+a^2 c x^2)^3 \text {arcsinh}(a x)^3 \, dx\) [328]
3.4.29
\(\int (c+a^2 c x^2)^2 \text {arcsinh}(a x)^3 \, dx\) [329]
3.4.30
\(\int (c+a^2 c x^2) \text {arcsinh}(a x)^3 \, dx\) [330]
3.4.31
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{c+a^2 c x^2} \, dx\) [331]
3.4.32
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{(c+a^2 c x^2)^2} \, dx\) [332]
3.4.33
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{(c+a^2 c x^2)^3} \, dx\) [333]
3.4.34
\(\int (c+a^2 c x^2)^{5/2} \text {arcsinh}(a x)^3 \, dx\) [334]
3.4.35
\(\int (c+a^2 c x^2)^{3/2} \text {arcsinh}(a x)^3 \, dx\) [335]
3.4.36
\(\int \sqrt {c+a^2 c x^2} \text {arcsinh}(a x)^3 \, dx\) [336]
3.4.37
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{\sqrt {c+a^2 c x^2}} \, dx\) [337]
3.4.38
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{(c+a^2 c x^2)^{3/2}} \, dx\) [338]
3.4.39
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{(c+a^2 c x^2)^{5/2}} \, dx\) [339]
3.4.40
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{(c+a^2 c x^2)^{7/2}} \, dx\) [340]
3.4.41
\(\int \genfrac {}{}{}{}{x^m \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx\) [341]
3.4.42
\(\int \genfrac {}{}{}{}{x^4 \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx\) [342]
3.4.43
\(\int \genfrac {}{}{}{}{x^3 \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx\) [343]
3.4.44
\(\int \genfrac {}{}{}{}{x^2 \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx\) [344]
3.4.45
\(\int \genfrac {}{}{}{}{x \text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx\) [345]
3.4.46
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{\sqrt {1+a^2 x^2}} \, dx\) [346]
3.4.47
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{x \sqrt {1+a^2 x^2}} \, dx\) [347]
3.4.48
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{x^2 \sqrt {1+a^2 x^2}} \, dx\) [348]
3.4.49
\(\int \genfrac {}{}{}{}{\text {arcsinh}(a x)^3}{x^3 \sqrt {1+a^2 x^2}} \, dx\) [349]
3.4.50
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^3}{\text {arcsinh}(a x)} \, dx\) [350]
3.4.51
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^2}{\text {arcsinh}(a x)} \, dx\) [351]
3.4.52
\(\int \genfrac {}{}{}{}{c+a^2 c x^2}{\text {arcsinh}(a x)} \, dx\) [352]
3.4.53
\(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2) \text {arcsinh}(a x)} \, dx\) [353]
3.4.54
\(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2)^2 \text {arcsinh}(a x)} \, dx\) [354]
3.4.55
\(\int \genfrac {}{}{}{}{x^4 \sqrt {1+c^2 x^2}}{a+b \text {arcsinh}(c x)} \, dx\) [355]
3.4.56
\(\int \genfrac {}{}{}{}{x^3 \sqrt {1+c^2 x^2}}{a+b \text {arcsinh}(c x)} \, dx\) [356]
3.4.57
\(\int \genfrac {}{}{}{}{x^2 \sqrt {1+c^2 x^2}}{a+b \text {arcsinh}(c x)} \, dx\) [357]
3.4.58
\(\int \genfrac {}{}{}{}{x \sqrt {1+c^2 x^2}}{a+b \text {arcsinh}(c x)} \, dx\) [358]
3.4.59
\(\int \genfrac {}{}{}{}{\sqrt {1+c^2 x^2}}{a+b \text {arcsinh}(c x)} \, dx\) [359]
3.4.60
\(\int \genfrac {}{}{}{}{\sqrt {1+c^2 x^2}}{x (a+b \text {arcsinh}(c x))} \, dx\) [360]
3.4.61
\(\int \genfrac {}{}{}{}{\sqrt {1+c^2 x^2}}{x^2 (a+b \text {arcsinh}(c x))} \, dx\) [361]
3.4.62
\(\int \genfrac {}{}{}{}{\sqrt {1+c^2 x^2}}{x^3 (a+b \text {arcsinh}(c x))} \, dx\) [362]
3.4.63
\(\int \genfrac {}{}{}{}{\sqrt {1+c^2 x^2}}{x^4 (a+b \text {arcsinh}(c x))} \, dx\) [363]
3.4.64
\(\int \genfrac {}{}{}{}{x^3 (1+c^2 x^2)^{3/2}}{a+b \text {arcsinh}(c x)} \, dx\) [364]
3.4.65
\(\int \genfrac {}{}{}{}{x^2 (1+c^2 x^2)^{3/2}}{a+b \text {arcsinh}(c x)} \, dx\) [365]
3.4.66
\(\int \genfrac {}{}{}{}{x (1+c^2 x^2)^{3/2}}{a+b \text {arcsinh}(c x)} \, dx\) [366]
3.4.67
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{3/2}}{a+b \text {arcsinh}(c x)} \, dx\) [367]
3.4.68
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{3/2}}{x (a+b \text {arcsinh}(c x))} \, dx\) [368]
3.4.69
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{3/2}}{x^2 (a+b \text {arcsinh}(c x))} \, dx\) [369]
3.4.70
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{3/2}}{x^3 (a+b \text {arcsinh}(c x))} \, dx\) [370]
3.4.71
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{3/2}}{x^4 (a+b \text {arcsinh}(c x))} \, dx\) [371]
3.4.72
\(\int \genfrac {}{}{}{}{x^3 (1+c^2 x^2)^{5/2}}{a+b \text {arcsinh}(c x)} \, dx\) [372]
3.4.73
\(\int \genfrac {}{}{}{}{x^2 (1+c^2 x^2)^{5/2}}{a+b \text {arcsinh}(c x)} \, dx\) [373]
3.4.74
\(\int \genfrac {}{}{}{}{x (1+c^2 x^2)^{5/2}}{a+b \text {arcsinh}(c x)} \, dx\) [374]
3.4.75
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{5/2}}{a+b \text {arcsinh}(c x)} \, dx\) [375]
3.4.76
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{5/2}}{x (a+b \text {arcsinh}(c x))} \, dx\) [376]
3.4.77
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{5/2}}{x^2 (a+b \text {arcsinh}(c x))} \, dx\) [377]
3.4.78
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{5/2}}{x^3 (a+b \text {arcsinh}(c x))} \, dx\) [378]
3.4.79
\(\int \genfrac {}{}{}{}{(1+c^2 x^2)^{5/2}}{x^4 (a+b \text {arcsinh}(c x))} \, dx\) [379]
3.4.80
\(\int \genfrac {}{}{}{}{x^4}{\sqrt {1+a^2 x^2} \text {arcsinh}(a x)} \, dx\) [380]
3.4.81
\(\int \genfrac {}{}{}{}{x^3}{\sqrt {1+a^2 x^2} \text {arcsinh}(a x)} \, dx\) [381]
3.4.82
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {1+a^2 x^2} \text {arcsinh}(a x)} \, dx\) [382]
3.4.83
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {1+a^2 x^2} \text {arcsinh}(a x)} \, dx\) [383]
3.4.84
\(\int \genfrac {}{}{}{}{x}{\sqrt {1+a^2 x^2} \text {arcsinh}(a x)} \, dx\) [384]
3.4.85
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+a^2 x^2} \text {arcsinh}(a x)} \, dx\) [385]
3.4.86
\(\int \genfrac {}{}{}{}{1}{x \sqrt {1+a^2 x^2} \text {arcsinh}(a x)} \, dx\) [386]
3.4.87
\(\int \genfrac {}{}{}{}{1}{x^2 \sqrt {1+a^2 x^2} \text {arcsinh}(a x)} \, dx\) [387]
3.4.88
\(\int \genfrac {}{}{}{}{x^5}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx\) [388]
3.4.89
\(\int \genfrac {}{}{}{}{x^4}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx\) [389]
3.4.90
\(\int \genfrac {}{}{}{}{x^3}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx\) [390]
3.4.91
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx\) [391]
3.4.92
\(\int \genfrac {}{}{}{}{x}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx\) [392]
3.4.93
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx\) [393]
3.4.94
\(\int \genfrac {}{}{}{}{1}{x \sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx\) [394]
3.4.95
\(\int \genfrac {}{}{}{}{1}{x^2 \sqrt {1+c^2 x^2} (a+b \text {arcsinh}(c x))} \, dx\) [395]
3.4.96
\(\int \genfrac {}{}{}{}{x^2}{(1+c^2 x^2)^{3/2} (a+b \text {arcsinh}(c x))} \, dx\) [396]
3.4.97
\(\int \genfrac {}{}{}{}{x}{(1+c^2 x^2)^{3/2} (a+b \text {arcsinh}(c x))} \, dx\) [397]
3.4.98
\(\int \genfrac {}{}{}{}{1}{(1+c^2 x^2)^{3/2} (a+b \text {arcsinh}(c x))} \, dx\) [398]
3.4.99
\(\int \genfrac {}{}{}{}{1}{x (1+c^2 x^2)^{3/2} (a+b \text {arcsinh}(c x))} \, dx\) [399]
3.4.100
\(\int \genfrac {}{}{}{}{1}{x^2 (1+c^2 x^2)^{3/2} (a+b \text {arcsinh}(c x))} \, dx\) [400]
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