What is the integral of xsin(8-x) ?

The integral of xsin(8-x) is xcos(8-x)+sin(8-x)+C

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integral of xsin(8-x)

\int x sin (8 - x) d x

x cos (8 - x) + sin (8 - x) + C

Solution steps

\int x sin (8 - x) d x

Apply Integration By Parts

: x cos (8 - x) - \int cos (8 - x) d x

= x cos (8 - x) - \int cos (8 - x) d x

\int cos (8 - x) d x = - sin (8 - x)

= x cos (8 - x) - (- sin (8 - x))

Simplify

= x cos (8 - x) + sin (8 - x)

Add a constant to the solution

= x cos (8 - x) + sin (8 - x) + C

x \to 0 lim (\frac{2 - 2}{2})

\int_{0}^{3} x sin (3 - x) d x

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

y = 4 x - x^{2}, y = x, x = 3

\frac{12 x}{x ^{2} - 4}

What is the integral of xsin(8-x) ?
The integral of xsin(8-x) is xcos(8-x)+sin(8-x)+C