Originally Posted by

**Gusbob** I've been studying for a integration and volumes test. I can do most of them but these few are giving me headaches. You don't have to solve them for me, just tell me what I need to do. Any help is appreciated.

1)

$\displaystyle \int \sqrt{16+x^2} \,dx$

I know I need to substitute $\displaystyle x = 4\,tan\,\theta \Rightarrow dx = 4\,sec^2\theta \,d\theta$

$\displaystyle \int 4sec\theta \bullet 4sec^2\theta \,d\theta$

=$\displaystyle \int 16 sec^3\theta\,d\theta$

I don't know how to go on from here.

The answer is $\displaystyle \frac{1}{2}x\sqrt{16+x^2} + 8 ln (x+\sqrt{16+x^2})$

2)

$\displaystyle \int \frac{1}{x^2\sqrt{x-1}}dx$

I've tried letting $\displaystyle u= \sqrt{x-1}$, but got nowhere from that.

3)

$\displaystyle \int_0^{\frac{\pi}{2}} \sqrt{1+sin\,2x}\, dx$

no clue