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The power of a product is equal to the product of it's factors raised to the same power
Learn how to solve trigonometric integrals problems step by step online.
$\int\sin\left(x\right)^4\cos\left(x\right)^4dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int((sin(x)cos(x))^4)dx. The power of a product is equal to the product of it's factors raised to the same power. 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).