What is the integral of x^2sin(1-x) ?

The integral of x^2sin(1-x) is x^2cos(1-x)+2(xsin(1-x)-cos(1-x))+C

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integral of x^2sin(1-x)

\int x^{2} sin (1 - x) d x

x^{2} cos (1 - x) + 2 (x sin (1 - x) - cos (1 - x)) + C

Solution steps

\int x^{2} sin (1 - x) d x

Apply Integration By Parts

: x^{2} cos (1 - x) - \int 2 x cos (1 - x) d x

= x^{2} cos (1 - x) - \int 2 x cos (1 - x) d x

\int 2 x cos (1 - x) d x = - 2 (x sin (1 - x) - cos (1 - x))

= x^{2} cos (1 - x) - (- 2 (x sin (1 - x) - cos (1 - x)))

Simplify

= x^{2} cos (1 - x) + 2 (x sin (1 - x) - cos (1 - x))

Add a constant to the solution

= x^{2} cos (1 - x) + 2 (x sin (1 - x) - cos (1 - x)) + C

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What is the integral of x^2sin(1-x) ?
The integral of x^2sin(1-x) is x^2cos(1-x)+2(xsin(1-x)-cos(1-x))+C