Can x = a*sinh(t) be used for solving \int (1/((\sqrt{(x^2)+(a^2)}))^(3/2)*dx)?

[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

 

[paulfr]

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

Is that correct ?

 

[zahero_2007]

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

 

[paulfr]

Attached is the solution with z=3
Cheers

 

[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

 

[dextercioby]

Try x=a\sinh t.