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Simplify the expression
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$\int\cos\left(x\right)^{6}\sin\left(x\right)^{3}dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(x)^4cos(x)^5tan(x)cot(x)^2)dx. Simplify the expression. 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=6 and n=3. Simplify the expression. The integral \frac{2}{9}\int\sin\left(x\right)\cos\left(x\right)^{6}dx results in: \frac{-2\cos\left(x\right)^{7}}{63}.