[SOLVED] Trig Substitution Integral

Integrate.

$\displaystyle \int \frac{3}{x^2\sqrt{100-sin x^2}} dx$

Here is what I have done (I left out all my early steps):

$\displaystyle \int \frac{30 cos\theta d\theta}{(10sin\theta)^2 (\sqrt{100-sin ^2\theta)}}$

$\displaystyle

\int \frac{30 cos\theta d\theta}{100(sin^2\theta) \cdot (10\sqrt{1-sin ^2 \theta}}$

$\displaystyle

\int \frac{30 cos\theta d\theta}{1000sin^2\theta \sqrt{cos ^2 \theta}}$

$\displaystyle = \frac{30}{1000} \int \frac{1}{sin^2 \theta} d\theta$

$\displaystyle

= \frac{30}{1000} \int \frac{2}{1-cos(2\theta)} d\theta$

Can someone please check this for me? Should I do a u sub with $\displaystyle 2\theta$? Thanks!!