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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. We can solve the integral \int144\cos\left(3x\right)^{2}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 3x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.