Integration by substitution

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

  • #2
192
3
So the problem is
Integral ( x^2 + a^2 ) ^ (-3/4) dx ?

Is that correct ?
 
  • #3
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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  • #4
192
3
Attached is the solution with z=3
Cheers
 

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  • #5
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
dextercioby
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Try [itex] x=a\sinh t [/itex].
 

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