# Integration by substitution

## Main Question or Discussion Point

Hi , I solved $\int (1/((\sqrt{(x^2)+(a^2)}))^(3/2)*dx)$ using the substitution x = a*tan($\varphi$ I wonder if there are other methods to solve this problem?
* (2/3) is the power on the radical function

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So the problem is
Integral ( x^2 + a^2 ) ^ (-3/4) dx ?

Is that correct ?

So the problem is
Integral ( x^2 + a^2 ) ^ (-3/4) dx ?

Is that correct ?
Integral ( x^2 + z^2 )^(-3/2)dx I'm sorry I wrote the integral wrong in the first post

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Attached is the solution with z=3
Cheers

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Thanks paulfr but I already said that I solved it with the same substitution x=a*tan(u). I'm asking whether another method exist to solve the integral

dextercioby
Try $x=a\sinh t$.