The value of $\int\frac{\sin(3x)}{\cos(7x)\cos(4x)}$

Question

The integral is $\int\frac{\sin3x}{\cos7x\cos4x}$

I have tried sum to product rule and $\sin3x$ formula:
$\int\frac{3\sin x-4\sin^3 x}{\frac{1}{2}(\cos3x+\cos11x)}$

How should I proceed further?

Answer 1

$$\frac{\sin 3x}{\cos 7x\cos 4x} = \frac{\sin (7x-4x)}{\cos 7x\cos 4x}=\frac{\sin 7x\cos 4x - \cos 7x \sin 4x}{\cos 7x \cos 4x} = \tan 7x - \tan 4x$$

I think you can take it from here.