- #1

JulieK

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- 0

[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
- Start date

- #1

JulieK

- 50

- 0

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

where a and b are constants.

- #2

pasmith

Homework Helper

- 2,332

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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

- 1,221

- 78

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

- #4

HakimPhilo

- 77

- 10

- #5

TheDemx27

Gold Member

- 170

- 13

Code:

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

Code:

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

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