Question

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

Answer 1

What method you have in mind?

Answer 2

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

Answer 3

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

Answer 4

Partial fractions?

Answer 5

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

Answer 6

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

Answer 7

oh and how would you do that?

Answer 8

Let
\[x=asec(\theta)\]

Answer 9

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

Answer 10

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

Answer 11

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