# Need integral help, i think its trig sub., thanks!

1. May 30, 2014

### klawlor419

$$\int_{0}^{a}\frac{x}{(x^2+z^2)^\frac{3}{2}}dx$$

Hi all, I'm stuck on this one. Sure theres an easier way to do it. Don't have my calc book currently. Thanks!

2. May 30, 2014

Put x2 = t.

3. May 30, 2014

### klawlor419

Got it with the trig sub $$x=z \tan{\theta}$$
Thanks!!

4. May 30, 2014

No, that substitution isn't convenient,

If you substitute x2 = t, you would get the numerator as dt (since dt= 2xdx)

5. May 30, 2014

### klawlor419

Thanks! That is slightly easier!

6. May 30, 2014

### HallsofIvy

I would have used $t= x^2+ z^2$ so that $dt= 2x dx$, $(1/2)dt= xdx$.

The integral becomes
$$\frac{1}{2}\int_{z^2}^{z^2+ a^2} t^{-3/2}dt$$

7. May 30, 2014

### klawlor419

Thanks! Thats slightly easier still!