Final Answer
Step-by-step Solution
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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 $x=z$ and $n=6$
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$\frac{-\sin\left(z\right)^{5}\cos\left(z\right)}{6}+\frac{5}{6}\int\sin\left(z\right)^{4}dz$
Learn how to solve special products problems step by step online. Solve the trigonometric integral int(sin(z)^6)dz. 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 x=z and n=6. The integral \frac{5}{6}\int\sin\left(z\right)^{4}dz results in: \frac{-5\sin\left(z\right)^{3}\cos\left(z\right)}{24}+\frac{5}{8}\left(\frac{z}{2}-\frac{1}{4}\sin\left(2z\right)\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.