Learn how to solve problems step by step online. Solve the trigonometric integral int(cos(20x)^3)dx. 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=20x. Expand the integral \int\left(\cos\left(20x\right)-\cos\left(20x\right)\sin\left(20x\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\cos\left(20x\right)dx results in: \frac{1}{20}\sin\left(20x\right). The integral \int-\cos\left(20x\right)\sin\left(20x\right)^2dx results in: \frac{-\sin\left(20x\right)^{3}}{60}.

Solve the trigonometric integral int(cos(20x)^3)dx