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

The integral of-3xsin(2x+2) is -3(-1/2 xcos(2x+2)+1/4 sin(2x+2))+C

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integral of-3xsin(2x+2)

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 3 \cdot \int x sin (2 x + 2) d x

Apply Integration By Parts

= - 3 (- \frac{1}{2} x cos (2 x + 2) - \int - \frac{1}{2} cos (2 x + 2) d x)

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

= - 3 (- \frac{1}{2} x cos (2 x + 2) - (- \frac{1}{4} sin (2 x + 2)))

Simplify

= - 3 (- \frac{1}{2} x cos (2 x + 2) + \frac{1}{4} sin (2 x + 2))

Add a constant to the solution

= - 3 (- \frac{1}{2} x cos (2 x + 2) + \frac{1}{4} sin (2 x + 2)) + C

What is the integral of-3xsin(2x+2) ?
The integral of-3xsin(2x+2) is -3(-1/2 xcos(2x+2)+1/4 sin(2x+2))+C