Evaluate the following integral: $$\displaystyle \int\dfrac{dx}{\left(\dfrac{1}{x}-\dfrac{1}{a}\right)}$$ Where $a$ is an arbitrary constant.
How do I solve this?
I tried the substitution $$x=a\cos \theta$$
But that got me here (i.e. no where): $$\displaystyle a^{3/2}\int\dfrac{-\sqrt {\cos\theta}.\sin\theta.d\theta}{\sqrt{1-\cos\theta}}$$
How do I simplify this further?