What is the integral of xsin(x)x ?

The integral of xsin(x)x is -x^2cos(x)+2(xsin(x)+cos(x))+C

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integral of xsin(x)x

\int x sin (x) x d x

- x^{2} cos (x) + 2 (x sin (x) + cos (x)) + C

Solution steps

\int x sin (x) x d x

Apply Integration By Parts

: - x^{2} cos (x) - \int - 2 x cos (x) d x

= - x^{2} cos (x) - \int - 2 x cos (x) d x

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

= - x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))

Simplify

= - x^{2} cos (x) + 2 (x sin (x) + cos (x))

Add a constant to the solution

= - x^{2} cos (x) + 2 (x sin (x) + cos (x)) + C

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What is the integral of xsin(x)x ?
The integral of xsin(x)x is -x^2cos(x)+2(xsin(x)+cos(x))+C