What is the integral of (2x+3)sin(x) ?

The integral of (2x+3)sin(x) is -cos(x)(2x+3)+2sin(x)+C

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integral of (2x+3)sin(x)

\int (2 x + 3) sin (x) d x

- cos (x) (2 x + 3) + 2 sin (x) + C

Solution steps

\int (2 x + 3) sin (x) d x

Apply Integration By Parts

: - cos (x) (2 x + 3) - \int - 2 cos (x) d x

= - cos (x) (2 x + 3) - \int - 2 cos (x) d x

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

= - cos (x) (2 x + 3) - (- 2 sin (x))

Simplify

= - cos (x) (2 x + 3) + 2 sin (x)

Add a constant to the solution

= - cos (x) (2 x + 3) + 2 sin (x) + C

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What is the integral of (2x+3)sin(x) ?
The integral of (2x+3)sin(x) is -cos(x)(2x+3)+2sin(x)+C