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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 $x=t$ and $n=4$
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$\frac{-\sin\left(t\right)^{3}\cos\left(t\right)}{4}+\frac{3}{4}\int\sin\left(t\right)^{2}dt$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(t)^4)dt. 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=t and n=4. The integral \frac{3}{4}\int\sin\left(t\right)^{2}dt results in: \frac{3}{8}t-\frac{3}{16}\sin\left(2t\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.