I have following integration:
$$ \int {\frac{dx} {x + {\sqrt{ 1- x^{2} }}} } $$
I'm trying to calculate it by letting x=cos(t) , dx=-sin(t)dt , and I got a very long result which is incorrect.
However, the correct answer is:
$$ {\frac {1} {2}} ( arcsin(x) + ln|x+{\sqrt{1-x^2}}| ) + C $$
So, how can I calculate it?