Learn how to solve problems step by step online. Solve the trigonometric integral int(2cos(8x)^3)dx. The integral of a function times a constant (2) is equal to the constant times the integral of the function. Apply the formula: \int\cos\left(\theta \right)^3dx=\int\left(\cos\left(\theta \right)-\cos\left(\theta \right)\sin\left(\theta \right)^2\right)dx, where x=8x. Expand the integral \int\left(\cos\left(8x\right)-\cos\left(8x\right)\sin\left(8x\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral 2\int\cos\left(8x\right)dx results in: \frac{1}{4}\sin\left(8x\right).

Solve the trigonometric integral int(2cos(8x)^3)dx