- #1

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[itex]\int\left(\frac{\mathrm{arcsinh}(ax)}{ax}\right)^{b}dx[/itex]

where a and b are constants.

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- Thread starter JulieK
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- #1

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[itex]\int\left(\frac{\mathrm{arcsinh}(ax)}{ax}\right)^{b}dx[/itex]

where a and b are constants.

- #2

pasmith

Homework Helper

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\int \left(\frac{\mathrm{arcsinh}(ax)}{ax}\right)^b\,dx = \int \left(\frac{t}{\sinh t}\right)^b \frac{\cosh t}{a}\,dt \\

= \left[ \frac{1}{a(1-b)}\frac{t^b}{(\sinh t)^{b-1}}\right]

+ \frac{b}{a(b - 1)} \int \left(\frac{t}{\sinh t}\right)^{b-1}\,dt \\

[/tex] on integration by parts. Unfortunately that seems to be as far as one can get.

- #3

Philip Wood

Gold Member

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The wonderful Wolfram online integrator can't do it, so there's not much hope...

- #4

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- #5

TheDemx27

Gold Member

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Code:

`Integrate[((ArcSinh[a * x])/ a * x)^b, x]`

Code:

`\[Integral]((x ArcSinh[a x])/a)^b \[DifferentialD]x`

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