how to find the integral of 1/(x^(3)sqrt(x^2-1))

Question

.sam. · Answer

What method you have in mind?

.sam. · Answer

$$\int\limits \frac{1}{x^3 \sqrt{x^2-1}} \, dx$$

anonymous · Answer

First impression: trig sub. I haven't worked it out for myself, but that's what I would try.

anonymous · Answer

Partial fractions?

anonymous · Answer

Oh no, I suppose we do use the u-substitution

.sam. · Answer

I dont think you can u-sub, trig sub will be the easiest way

anonymous · Answer

oh and how would you do that?

.sam. · Answer

Let 
$$x=asec(\theta)$$

anonymous · Answer

oh Okay. That makes sense. I'll try to work it out. Thank you

.sam. · Answer

When you worked all those trigs you'll end up
$$\int\limits \cos^2 \theta d \theta$$
Then use $\cos(2\theta)=1-2\cos^2(\theta)$ and simplify

anonymous · Answer

This is what I should get $$\frac{ \sqrt{(x ^{2}-1)} }{ 2x ^{2} }$$-$$\frac{ 1 }{ 2 }\arctan(\frac{ 1 }{ \sqrt{x ^{2}-1} })$$