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$\int\left(12\cos\left(3x\right)+6\cos\left(3x\right)^2+\cos\left(3x\right)^3\right)^2dx$
Learn how to solve problems step by step online. Integrate the function (12cos(3x)+6cos(3x)^2cos(3x)^3)^2. Find the integral. Rewrite the integrand \left(12\cos\left(3x\right)+6\cos\left(3x\right)^2+\cos\left(3x\right)^3\right)^2 in expanded form. Expand the integral \int\left(144\cos\left(3x\right)^{2}+144\cos\left(3x\right)^{3}+36\cos\left(3x\right)^{4}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. Multiply the single term 48 by each term of the polynomial \left(\frac{1}{2}\cdot 3x+\frac{1}{4}\sin\left(6x\right)\right).