Hi, I'm new and have a few problems that I'm beating my head over. Hopefully you all can help me understand. Thanks in advance!

Number 1:

$\displaystyle \int \frac {x^2} {\sqrt {9-x^2}}dx$

Here's what I did with it, and where I ended up. I'm not really sure if I've messed up or just need to keep going forward. If I am on the right track...I can't figure out where to go next.

$\displaystyle x=3\sin\theta$

$\displaystyle dx=3 \cos \theta d \theta$

$\displaystyle \int \frac {9\sin^2{\theta} 3 \cos{ \theta}d \theta}{ \sqrt{9(1-sin^2{ \theta})}}$

$\displaystyle \int \frac {9\sin^2{\theta} 3 \cos{ \theta}d \theta}{ 3\cos{\theta}}$

$\displaystyle \int {9\sin^2{\theta} d \theta}$

$\displaystyle 9(\frac {1}{2} \theta - \frac {1}{4} \sin 2 \theta) +C$

Number 2:

$\displaystyle \int \frac {3x^2 -4x-2}{(x-1)^2(x+2)}dx$

I'm pretty sure that I've made a dumb mistake on this one, probably an obvious one. Something doesn't feel right... Used partial fractions for the first bit.

$\displaystyle 3x^2 -4x-2=A(x+2) + B(x-1)(x+2) + C (x-1)^2$

$\displaystyle A=-1 \ \ \

B=1 \ \ \

C=2$

$\displaystyle \int ( \frac {-1}{(x-1)^2} +\frac {1}{(x-1)} +\frac {2}{(x+2)})dx$

$\displaystyle \frac {1}{(x-1)} + \ln(x-1) + 2\ln(x+2) +C$

Number 3:

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

Ok...I'm pretty sure this one starts with a substitution, but I'm totally lost with it. Help?

Again, thanks for looking over all of this, I hope it all makes sense.