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

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

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integral of (x-1)sin(x)

\int (x - 1) sin (x) d x

- cos (x) (x - 1) + sin (x) + C

Solution steps

\int (x - 1) sin (x) d x

Apply Integration By Parts

: - cos (x) (x - 1) - \int - cos (x) d x

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

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

= - cos (x) (x - 1) - (- sin (x))

Simplify

= - cos (x) (x - 1) + sin (x)

Add a constant to the solution

= - cos (x) (x - 1) + sin (x) + C

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