What is the integral of xsin(5-x) ?

The integral of xsin(5-x) is xcos(5-x)+sin(5-x)+C

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integral of xsin(5-x)

\int x sin (5 - x) d x

x cos (5 - x) + sin (5 - x) + C

Solution steps

\int x sin (5 - x) d x

Apply Integration By Parts

= x cos (5 - x) - \int cos (5 - x) d x

\int cos (5 - x) d x = - sin (5 - x)

= x cos (5 - x) - (- sin (5 - x))

Simplify

= x cos (5 - x) + sin (5 - x)

Add a constant to the solution

= x cos (5 - x) + sin (5 - x) + C

in v erse l a pl a ce \frac{8}{s}

y^{^{''}} + y^{^{'}} - 20 y = - 1200 t^{3}

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What is the integral of xsin(5-x) ?
The integral of xsin(5-x) is xcos(5-x)+sin(5-x)+C