$$ \int \frac{(\cos 9x + \cos6x)}{2 \cos 5x - 1} dx $$
I know that it simplifies to $ \cos x + \cos 4x $ but I have no idea how to do that. I tried expanding $\cos 9x $ and $\cos 6x$ by using the formulas for $\cos 3x$ and $\cos 2x$. There is nothing i could think to simplify the $\cos 5x$ in the denominator
How to proceed while simplifying larger multiples to lower.
Is the any other way than simplifying the expression to calculate the integral?