What is the integral of xsin(4-x) ?

The integral of xsin(4-x) is xcos(4-x)+sin(4-x)+C

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integral of xsin(4-x)

\int x sin (4 - x) d x

x cos (4 - x) + sin (4 - x) + C

Solution steps

\int x sin (4 - x) d x

Apply Integration By Parts

: x cos (4 - x) - \int cos (4 - x) d x

= x cos (4 - x) - \int cos (4 - x) d x

\int cos (4 - x) d x = - sin (4 - x)

= x cos (4 - x) - (- sin (4 - x))

Simplify

= x cos (4 - x) + sin (4 - x)

Add a constant to the solution

= x cos (4 - x) + sin (4 - x) + C

\int ln^{2} (x) d x

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\int \frac{1}{( D \cdot E ) - ( D \cdot \frac{F}{G} x )} d x

\frac{d}{d x} ((- 2 x^{3} + 2 x^{2})^{4})

\frac{d}{d x} ((x + 2)^{- 1})

What is the integral of xsin(4-x) ?
The integral of xsin(4-x) is xcos(4-x)+sin(4-x)+C