I'm having trouble with trig substitution. This is what I've done so far, but I'm not sure if I did everything right. This is the integral: $$\int \frac{x^2}{(1+x^2)^\frac{3}{2}}$$
and my substitution is: $x= \tan\Theta$
$$\int \frac{\tan\Theta ^2}{(\sqrt{\sec\Theta ^2})^3}\sec\Theta ^2d\Theta $$
$$\int \frac{\sec\Theta ^2-1}{\sec\Theta }$$
$$\int \sec\Theta -\int \cos\Theta $$
$$(\ln(\sec\Theta +\tan\Theta ))-(\sin\Theta)$$
$$\ln(\frac{1}{\sqrt{1-x^2}}+ \frac{x}{\sqrt{1-x^2}}) - x + C$$
Thanks!