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Step-by-step Solution

Integrate cos(x)^2sin(x)^2

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asin
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asinh
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Answer

$\frac{1}{4}\sin\left(2x\right)-\left(\frac{1}{4}\sin\left(2x\right)+\frac{1}{8}\left(x+\frac{1}{4}\sin\left(4x\right)\right)\right)+\frac{1}{4}x+C_0$

Step-by-step explanation

Problem to solve:

$\int\cos\left(x\right)^2\sin\left(x\right)^2dx$
1

Applying the trigonometric identity: $\sin^2(\theta)=1-\cos(\theta)^2$

$\int\cos\left(x\right)^2\left(1-\cos\left(x\right)^2\right)dx$
2

Multiplying polynomials $\cos\left(x\right)^2$ and $1+-\cos\left(x\right)^2$

$\int\left(\cos\left(x\right)^2-\cos\left(x\right)^{4}\right)dx$

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Answer

$\frac{1}{4}\sin\left(2x\right)-\left(\frac{1}{4}\sin\left(2x\right)+\frac{1}{8}\left(x+\frac{1}{4}\sin\left(4x\right)\right)\right)+\frac{1}{4}x+C_0$

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