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$\int\cos\left(2x\right)^2\cos\left(2x\right)dx$
Learn how to solve problems step by step online. Integrate the function cos(2x)^2cos(2x). Find the integral. When multiplying exponents with same base you can add the exponents: \cos\left(2x\right)^2\cos\left(2x\right). 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=2x. Expand the integral \int\left(\cos\left(2x\right)-\cos\left(2x\right)\sin\left(2x\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.