Need help with the integral $\int \frac{2\tan(x)+3}{5\sin^2(x)+4}\,dx$ I'm having a problem resolving the following integral, spent almost all day trying.
Any help would be appreciated.
$$\int \frac{2\tan(x)+3}{5\sin^2(x)+4}\,dx$$

Try $t=\tan(x/2)$. This leads to $\sin(x)=\frac{2t}{1+t^2}$, $\tan(x)=\frac{2t}{1-t^2}$ and finally $dx = \frac{2\,dt}{1+t^2}$. Then use a classical partial fraction expansion.
