What is the integral of xsin(6-x) ?

The integral of xsin(6-x) is xcos(6-x)+sin(6-x)+C

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integral of xsin(6-x)

\int x sin (6 - x) d x

x cos (6 - x) + sin (6 - x) + C

Solution steps

\int x sin (6 - x) d x

Apply Integration By Parts

: x cos (6 - x) - \int cos (6 - x) d x

= x cos (6 - x) - \int cos (6 - x) d x

\int cos (6 - x) d x = - sin (6 - x)

= x cos (6 - x) - (- sin (6 - x))

Simplify

= x cos (6 - x) + sin (6 - x)

Add a constant to the solution

= x cos (6 - x) + sin (6 - x) + C

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What is the integral of xsin(6-x) ?
The integral of xsin(6-x) is xcos(6-x)+sin(6-x)+C