# What is the integral of #int sin^2(x)cos^4(x) dx#?

Applying integral reduction,

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To integrate ( \int \sin^2(x) \cos^4(x) , dx ), you can use the trigonometric identity ( \sin^2(x) = \frac{1 - \cos(2x)}{2} ) and ( \cos^4(x) = \left(\frac{1 + \cos(2x)}{2}\right)^2 ). Then substitute these identities into the integral and simplify. After simplification, the integral becomes ( \frac{1}{8}x - \frac{1}{32}\sin(4x) + C ), where ( C ) is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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