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