# What is the value of $\int\frac{\sin(3x)}{\cos(7x)\cos(4x)}$

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?

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