1. ## u substitution

I would like to evaluate this integral using u substitution, I tried

let u = sin x

but that did not seem to do anything, should I be changing the sec^2x - 1 to something else?

Any help is appreciated!

2. Do you know that: $sec^{2}x-tan^{2}x=1$ ??

3. Originally Posted by DarK
I would like to evaluate this integral using u substitution, I tried

let u = sin x

but that did not seem to do anything, should I be changing the sec^2x - 1 to something else?

Any help is appreciated!
In integrals like this the following substitution works 'almost always'...

$\displaystyle t= \tan \frac{x}{2} \implies dx= 2\ \frac{dt}{1+t^{2}}, \sin x = \frac{2t}{1+t^{2}}, \cos x = \frac{1-t^{2}}{1+t^{2}}$

Kind regards

$\chi$ $\sigma$

4. sec(x)= 1/cos(x) so sec^2(x)= 1/cos^2(x). I presume you know how to "change" cos(x) into sin(x).

5. Let $\displaystyle u = \sec(x)$. That substitution kills the integral on one-go.