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

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

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integral of xcos(3x+2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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