What is the integral of (5x-2)sin(x) ?

The integral of (5x-2)sin(x) is -cos(x)(5x-2)+5sin(x)+C

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integral of (5x-2)sin(x)

\int (5 x - 2) sin (x) d x

- cos (x) (5 x - 2) + 5 sin (x) + C

Solution steps

\int (5 x - 2) sin (x) d x

Apply Integration By Parts

: - cos (x) (5 x - 2) - \int - 5 cos (x) d x

= - cos (x) (5 x - 2) - \int - 5 cos (x) d x

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

= - cos (x) (5 x - 2) - (- 5 sin (x))

Simplify

= - cos (x) (5 x - 2) + 5 sin (x)

Add a constant to the solution

= - cos (x) (5 x - 2) + 5 sin (x) + C

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What is the integral of (5x-2)sin(x) ?
The integral of (5x-2)sin(x) is -cos(x)(5x-2)+5sin(x)+C