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3.5
Integrals 401 to 474
3.5.1
\(\int (a+b \text {ArcSin}(1+d x^2))^4 \, dx\) [401]
3.5.2
\(\int (a+b \text {ArcSin}(1+d x^2))^3 \, dx\) [402]
3.5.3
\(\int (a+b \text {ArcSin}(1+d x^2))^2 \, dx\) [403]
3.5.4
\(\int (a+b \text {ArcSin}(1+d x^2)) \, dx\) [404]
3.5.5
\(\int \genfrac {}{}{}{}{1}{a+b \text {ArcSin}(1+d x^2)} \, dx\) [405]
3.5.6
\(\int \genfrac {}{}{}{}{1}{(a+b \text {ArcSin}(1+d x^2))^2} \, dx\) [406]
3.5.7
\(\int \genfrac {}{}{}{}{1}{(a+b \text {ArcSin}(1+d x^2))^3} \, dx\) [407]
3.5.8
\(\int (a-b \text {ArcSin}(1-d x^2))^4 \, dx\) [408]
3.5.9
\(\int (a-b \text {ArcSin}(1-d x^2))^3 \, dx\) [409]
3.5.10
\(\int (a-b \text {ArcSin}(1-d x^2))^2 \, dx\) [410]
3.5.11
\(\int (a-b \text {ArcSin}(1-d x^2)) \, dx\) [411]
3.5.12
\(\int \genfrac {}{}{}{}{1}{a-b \text {ArcSin}(1-d x^2)} \, dx\) [412]
3.5.13
\(\int \genfrac {}{}{}{}{1}{(a-b \text {ArcSin}(1-d x^2))^2} \, dx\) [413]
3.5.14
\(\int \genfrac {}{}{}{}{1}{(a-b \text {ArcSin}(1-d x^2))^3} \, dx\) [414]
3.5.15
\(\int \text {ArcSin}(1+x^2)^2 \, dx\) [415]
3.5.16
\(\int \text {ArcSin}(1-x^2)^2 \, dx\) [416]
3.5.17
\(\int (a+b \text {ArcSin}(1+d x^2))^{5/2} \, dx\) [417]
3.5.18
\(\int (a+b \text {ArcSin}(1+d x^2))^{3/2} \, dx\) [418]
3.5.19
\(\int \sqrt {a+b \text {ArcSin}(1+d x^2)} \, dx\) [419]
3.5.20
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \text {ArcSin}(1+d x^2)}} \, dx\) [420]
3.5.21
\(\int \genfrac {}{}{}{}{1}{(a+b \text {ArcSin}(1+d x^2))^{3/2}} \, dx\) [421]
3.5.22
\(\int \genfrac {}{}{}{}{1}{(a+b \text {ArcSin}(1+d x^2))^{5/2}} \, dx\) [422]
3.5.23
\(\int \genfrac {}{}{}{}{1}{(a+b \text {ArcSin}(1+d x^2))^{7/2}} \, dx\) [423]
3.5.24
\(\int (a-b \text {ArcSin}(1-d x^2))^{5/2} \, dx\) [424]
3.5.25
\(\int (a-b \text {ArcSin}(1-d x^2))^{3/2} \, dx\) [425]
3.5.26
\(\int \sqrt {a-b \text {ArcSin}(1-d x^2)} \, dx\) [426]
3.5.27
\(\int \genfrac {}{}{}{}{1}{\sqrt {a-b \text {ArcSin}(1-d x^2)}} \, dx\) [427]
3.5.28
\(\int \genfrac {}{}{}{}{1}{(a-b \text {ArcSin}(1-d x^2))^{3/2}} \, dx\) [428]
3.5.29
\(\int \genfrac {}{}{}{}{1}{(a-b \text {ArcSin}(1-d x^2))^{5/2}} \, dx\) [429]
3.5.30
\(\int \genfrac {}{}{}{}{1}{(a-b \text {ArcSin}(1-d x^2))^{7/2}} \, dx\) [430]
3.5.31
\(\int \genfrac {}{}{}{}{(a+b \text {ArcSin}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))^n}{1-c^2 x^2} \, dx\) [431]
3.5.32
\(\int \genfrac {}{}{}{}{(a+b \text {ArcSin}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))^3}{1-c^2 x^2} \, dx\) [432]
3.5.33
\(\int \genfrac {}{}{}{}{(a+b \text {ArcSin}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))^2}{1-c^2 x^2} \, dx\) [433]
3.5.34
\(\int \genfrac {}{}{}{}{a+b \text {ArcSin}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}})}{1-c^2 x^2} \, dx\) [434]
3.5.35
\(\int \genfrac {}{}{}{}{1}{(1-c^2 x^2) (a+b \text {ArcSin}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))} \, dx\) [435]
3.5.36
\(\int \genfrac {}{}{}{}{1}{(1-c^2 x^2) (a+b \text {ArcSin}(\genfrac {}{}{}{}{\sqrt {1-c x}}{\sqrt {1+c x}}))^2} \, dx\) [436]
3.5.37
\(\int e^x \text {ArcSin}(e^x) \, dx\) [437]
3.5.38
\(\int \text {ArcSin}(c e^{a+b x}) \, dx\) [438]
3.5.39
\(\int e^{\text {ArcSin}(a x)} x^3 \, dx\) [439]
3.5.40
\(\int e^{\text {ArcSin}(a x)} x^2 \, dx\) [440]
3.5.41
\(\int e^{\text {ArcSin}(a x)} x \, dx\) [441]
3.5.42
\(\int e^{\text {ArcSin}(a x)} \, dx\) [442]
3.5.43
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a x)}}{x} \, dx\) [443]
3.5.44
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a x)}}{x^2} \, dx\) [444]
3.5.45
\(\int e^{\text {ArcSin}(a x)^2} x^3 \, dx\) [445]
3.5.46
\(\int e^{\text {ArcSin}(a x)^2} x^2 \, dx\) [446]
3.5.47
\(\int e^{\text {ArcSin}(a x)^2} x \, dx\) [447]
3.5.48
\(\int e^{\text {ArcSin}(a x)^2} \, dx\) [448]
3.5.49
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a x)^2}}{x} \, dx\) [449]
3.5.50
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a x)^2}}{x^2} \, dx\) [450]
3.5.51
\(\int e^{\text {ArcSin}(a+b x)} x^3 \, dx\) [451]
3.5.52
\(\int e^{\text {ArcSin}(a+b x)} x^2 \, dx\) [452]
3.5.53
\(\int e^{\text {ArcSin}(a+b x)} x \, dx\) [453]
3.5.54
\(\int e^{\text {ArcSin}(a+b x)} \, dx\) [454]
3.5.55
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a+b x)}}{x} \, dx\) [455]
3.5.56
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a+b x)}}{x^2} \, dx\) [456]
3.5.57
\(\int e^{\text {ArcSin}(a+b x)^2} x^3 \, dx\) [457]
3.5.58
\(\int e^{\text {ArcSin}(a+b x)^2} x^2 \, dx\) [458]
3.5.59
\(\int e^{\text {ArcSin}(a+b x)^2} x \, dx\) [459]
3.5.60
\(\int e^{\text {ArcSin}(a+b x)^2} \, dx\) [460]
3.5.61
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a+b x)^2}}{x} \, dx\) [461]
3.5.62
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a+b x)^2}}{x^2} \, dx\) [462]
3.5.63
\(\int e^{\text {ArcSin}(a x)} (1-a^2 x^2)^{5/2} \, dx\) [463]
3.5.64
\(\int e^{\text {ArcSin}(a x)} (1-a^2 x^2)^{3/2} \, dx\) [464]
3.5.65
\(\int e^{\text {ArcSin}(a x)} \sqrt {1-a^2 x^2} \, dx\) [465]
3.5.66
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a x)}}{\sqrt {1-a^2 x^2}} \, dx\) [466]
3.5.67
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a x)}}{(1-a^2 x^2)^{3/2}} \, dx\) [467]
3.5.68
\(\int \genfrac {}{}{}{}{e^{\text {ArcSin}(a x)}}{(1-a^2 x^2)^{5/2}} \, dx\) [468]
3.5.69
\(\int \text {ArcSin}(\genfrac {}{}{}{}{c}{a+b x}) \, dx\) [469]
3.5.70
\(\int \genfrac {}{}{}{}{x}{\text {ArcSin}(\sin (x))} \, dx\) [470]
3.5.71
\(\int \genfrac {}{}{}{}{\text {ArcSin}(\sqrt {1+b x^2})^n}{\sqrt {1+b x^2}} \, dx\) [471]
3.5.72
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+b x^2} \text {ArcSin}(\sqrt {1+b x^2})} \, dx\) [472]
3.5.73
\(\int (\genfrac {}{}{}{}{x}{1-x^2}+\genfrac {}{}{}{}{1}{\sqrt {1-x^2} \text {ArcSin}(x)}) \, dx\) [473]
3.5.74
\(\int \genfrac {}{}{}{}{\sqrt {1-x^2}+x \text {ArcSin}(x)}{\text {ArcSin}(x)-x^2 \text {ArcSin}(x)} \, dx\) [474]
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