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

The integral of xsin(2x+1) is -1/2 xcos(2x+1)+1/4 sin(2x+1)+C

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integral of xsin(2x+1)

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

- \frac{1}{2} x cos (2 x + 1) + \frac{1}{4} sin (2 x + 1) + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{1}{2} cos (2 x + 1) d x = - \frac{1}{4} sin (2 x + 1)

= - \frac{1}{2} x cos (2 x + 1) - (- \frac{1}{4} sin (2 x + 1))

Simplify

= - \frac{1}{2} x cos (2 x + 1) + \frac{1}{4} sin (2 x + 1)

Add a constant to the solution

= - \frac{1}{2} x cos (2 x + 1) + \frac{1}{4} sin (2 x + 1) + C

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- 2744 - x^{3}

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What is the integral of xsin(2x+1) ?
The integral of xsin(2x+1) is -1/2 xcos(2x+1)+1/4 sin(2x+1)+C