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Apply the formula: $\int\sin\left(\theta \right)^ndx$$=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)}{n}+\frac{n-1}{n}\int\sin\left(\theta \right)^{\left(n-2\right)}dx$, where $n=5$
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$\frac{-\sin\left(x\right)^{4}\cos\left(x\right)}{5}+\frac{4}{5}\int\sin\left(x\right)^{3}dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(x)^5)dx. Apply the formula: \int\sin\left(\theta \right)^ndx=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)}{n}+\frac{n-1}{n}\int\sin\left(\theta \right)^{\left(n-2\right)}dx, where n=5. The integral \frac{4}{5}\int\sin\left(x\right)^{3}dx results in: \frac{-4\sin\left(x\right)^{2}\cos\left(x\right)}{15}-\frac{8}{15}\cos\left(x\right). Gather the results of all integrals. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.