Hello

Solve

$\displaystyle \int \frac{dx}{9sin^2(x)+4cos^2(x)}$

The substitution $\displaystyle u=tan(\frac{x}{2})$ maybe will solve it.

since it is used for the rational trigonometric function, especially which invloves sine and cosine.

But it changes it to a complicated rational function in u.

I believed, there is an easy way !