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

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

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integral of (2x+1)sin(x)

\int (2 x + 1) sin (x) d x

- cos (x) (2 x + 1) + 2 sin (x) + C

Solution steps

\int (2 x + 1) sin (x) d x

Apply Integration By Parts

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

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

= - cos (x) (2 x + 1) - (- 2 sin (x))

Simplify

= - cos (x) (2 x + 1) + 2 sin (x)

Add a constant to the solution

= - cos (x) (2 x + 1) + 2 sin (x) + C

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