What is the integral of-2xsin(-3x+1) ?

The integral of-2xsin(-3x+1) is -2(1/3 xcos(-3x+1)+1/9 sin(-3x+1))+C

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integral of-2xsin(-3x+1)

\int - 2 x sin (- 3 x + 1) d x

- 2 (\frac{1}{3} x cos (- 3 x + 1) + \frac{1}{9} sin (- 3 x + 1)) + C

Solution steps

\int - 2 x sin (- 3 x + 1) d x

Take the constant out:

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

= - 2 \cdot \int x sin (- 3 x + 1) d x

Apply Integration By Parts

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

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

\int \frac{1}{3} cos (- 3 x + 1) d x = - \frac{1}{9} sin (- 3 x + 1)

= - 2 (\frac{1}{3} x cos (- 3 x + 1) - (- \frac{1}{9} sin (- 3 x + 1)))

Simplify

= - 2 (\frac{1}{3} x cos (- 3 x + 1) + \frac{1}{9} sin (- 3 x + 1))

Add a constant to the solution

= - 2 (\frac{1}{3} x cos (- 3 x + 1) + \frac{1}{9} sin (- 3 x + 1)) + C

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What is the integral of-2xsin(-3x+1) ?
The integral of-2xsin(-3x+1) is -2(1/3 xcos(-3x+1)+1/9 sin(-3x+1))+C