How to solve integral arctan I solved  this integral: $$ \int_0^{\pi/2}\frac{dx}{5+4\cos x} $$ and I obtained  $\frac{2}{3} \arctan \frac{1}{3}$  is it correct? how do I find the answer in $\pi$?


and I obtained  $\frac{2}{3} \arctan \frac{1}{3}$  is it correct?

Yes, that is correct!

How do I find the answer in $\pi$?

What do you mean, "in $\pi$"?
Perhaps the model answer looks different (containing $\pi$)? You can use the property:
$$\boxed{\arctan a + \arctan \frac{1}{a} = \frac{\pi}{2}} \implies \color{blue}{\arctan\frac{1}{3} = \frac{\pi}{2}-\arctan 3 }$$
to rewrite as follows:
$$\frac{2}{3}\color{blue}{\arctan\frac{1}{3}} = \frac{2}{3}\left(\color{blue}{ \frac{\pi}{2}-\arctan 3} \right) = \frac{\pi}{3}-\frac{2}{3}\arctan 3$$
