Show the integral of dx/(1-x^2/a^2)

[chris_0101]

Homework Statement

Hi, I am having a bit of trouble visualizing the process of the following integral:

∫dx/(1-x^2/a^2)

The answer to this would be: atanh^-1$\frac{x}{a}$

if someone could show me this, that would be greatly appreciated.

Thanks

 

[obafgkmrns]

Substitute x/a = tanh θ and use the identity 1 - (tanh θ)^2 = 1/(cosh θ)^2.

 

[chris_0101]

thanks for the tip, I managed to solve the question.