# How do you find the integral of #x(sinx)^2#?

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To find the integral of (x(\sin{x})^2), you can use integration by parts method with (u = x) and (dv = (\sin{x})^2 dx). After finding the derivative of (u) and the antiderivative of (dv), apply the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

By integrating by parts, you'll eventually get:

[ \int x(\sin{x})^2 , dx = -x\sin{x}\cos{x} + \int \sin{x}\cos{x} , dx ]

Now, integrate (\sin{x}\cos{x}) using a trigonometric identity. The integral of (\sin{x}\cos{x}) is ((\sin{x})^2/2) + C.

Therefore, the integral of (x(\sin{x})^2) is:

[ -x\sin{x}\cos{x} + \frac{1}{2}(\sin{x})^2 + C ]

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