What is the integral of xsin(x) ?

The integral of xsin(x) is -xcos(x)+sin(x)+C

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integral of xsin(x)

integral

x sin (x)

- x cos (x) + sin (x) + C

Solution steps

\int x sin (x) d x

Apply Integration By Parts

: - x cos (x) - \int - cos (x) d x

= - x cos (x) - \int - cos (x) d x

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

= - x cos (x) - (- sin (x))

Simplify

= - x cos (x) + sin (x)

Add a constant to the solution

= - x cos (x) + sin (x) + C

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