Learn how to solve problems step by step online. Solve the trigonometric integral int(cos(x)cos(2nx))dx. Apply the rule of the product of two cosines \cos\left(a\right)\cdot\cos\left(b\right)=\frac{\cos\left(a+b\right)+\cos\left(a-b\right)}{2}. Take the constant \frac{1}{2} out of the integral. Expand the integral \int\left(\cos\left(x+2nx\right)+\cos\left(x-2nx\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \frac{1}{2}\int\cos\left(x+2nx\right)dx results in: \frac{\sin\left(x+2nx\right)}{2\left(1+2n\right)}.

Solve the trigonometric integral int(cos(x)cos(2nx))dx