# What is the integral of # x * cos^2 (x)#?

so we are looking at

as it's a composite term, we should do the red bit using IBP ie

here

so

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The integral of (x \cdot \cos^2(x)) with respect to (x) is:

[ \int x \cdot \cos^2(x) , dx = \frac{x}{2} + \frac{\sin(2x)}{4} + C ]

Where (C) is the constant of integration.

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