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Apply the formula: $\int\sin\left(\theta \right)^n\cos\left(\theta \right)^mdx$$=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)^{\left(m+1\right)}}{n+m}+\frac{n-1}{n+m}\int\sin\left(\theta \right)^{\left(n-2\right)}\cos\left(\theta \right)^mdx$, where $m=4$ and $n=4$
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$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)^{5}}{4+4}+\frac{4-1}{4+4}\int\sin\left(x\right)^{2}\cos\left(x\right)^4dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(x)^4cos(x)^4)dx. Apply the formula: \int\sin\left(\theta \right)^n\cos\left(\theta \right)^mdx=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)^{\left(m+1\right)}}{n+m}+\frac{n-1}{n+m}\int\sin\left(\theta \right)^{\left(n-2\right)}\cos\left(\theta \right)^mdx, where m=4 and n=4. Simplify the expression inside the integral. The integral \frac{3}{8}\int\sin\left(x\right)^{2}\cos\left(x\right)^4dx results in: \frac{1}{64}\cos\left(x\right)^{3}\sin\left(x\right)+\frac{9}{64}x+\frac{9}{128}\sin\left(2x\right)-\frac{1}{16}\cos\left(x\right)^{5}\sin\left(x\right)-\frac{15}{64}\left(\frac{1}{2}x+\frac{1}{4}\sin\left(2x\right)\right). Gather the results of all integrals.