# Integration by substitution

1. Sep 27, 2011

### zahero_2007

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

Last edited: Sep 27, 2011
2. Sep 27, 2011

### paulfr

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

Is that correct ?

3. Sep 28, 2011

### zahero_2007

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

Last edited: Sep 28, 2011
4. Sep 28, 2011

### paulfr

Attached is the solution with z=3
Cheers

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5. Sep 28, 2011

### zahero_2007

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

6. Sep 28, 2011

### dextercioby

Try $x=a\sinh t$.