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Simplify $\sin\left(3x\right)^2\cos\left(3x\right)$ into $\cos\left(3x\right)-\cos\left(3x\right)^{3}$ by applying trigonometric identities
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$\int\left(\cos\left(3x\right)-\cos\left(3x\right)^{3}\right)dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(3x)^2cos(3x))dx. Simplify \sin\left(3x\right)^2\cos\left(3x\right) into \cos\left(3x\right)-\cos\left(3x\right)^{3} by applying trigonometric identities. Expand the integral \int\left(\cos\left(3x\right)-\cos\left(3x\right)^{3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\cos\left(3x\right)dx results in: \frac{1}{3}\sin\left(3x\right). The integral \int-\cos\left(3x\right)^{3}dx results in: -\frac{1}{3}\sin\left(3x\right)+\frac{\sin\left(3x\right)^{3}}{9}.