Find the indefinite integral $\int \frac{25}{(3\cos(x)+4\sin(x))^2} dx$ > Find the indefinite integral: $$ \int\frac{25}{(3\cos(x)+4\sin(x))^2} dx$$ Obviously the first thing to is to expand the denominator but that doesn't help us that much. I have also tried applying the Weierstrass substitution but that lead to a black hole of algebra. I also notice the denominator has a $3$ and $4$ and the numerator has $25$ which mean a $3-4-5$ triangle might be related to this integral but I'm not to sure. Any help is appreciated :)

**Hint**. One may write $$ \int \frac{25}{(3\cos(x)+4\sin(x))^2} dx=\int \frac{25}{(3+4\tan(x))^2} \frac{dx}{\cos^2 x}=\int \frac{25}{(3+4u)^2} \:du $$ with $u=\tan x$.