i cant figure out the result of this integral using two methods:

int ((a^2)+(x^2))^(-3/2)dx

i used one method of substituting x with a*tan(theta).
can anyone figure out another method? simpler is better.

thanks

Question

i cant figure out the result of this integral using two methods:

int ((a^2)+(x^2))^(-3/2)dx

i used one method of substituting x with a*tan(theta).
can anyone figure out another method? simpler is better.

thanks

lochana · Answer

substitute x = a tan(theta)

anonymous · Answer

thankyou,
this is what i have do but exists another method?

lochana · Answer

have you found the solution?

anonymous · Answer

yes the result is 
$$\frac{ x }{ a^2\sqrt{a^2+x^2} } +c$$

but I want to use a method to compute the integral without using trigonometry

anonymous · Answer

if I use integration by parts how can I split the fuction:$$\int\limits_{}^{}f * g' dx$$