What is the integral of-2xcos(3x+4) ?

The integral of-2xcos(3x+4) is -2(1/3 xsin(3x+4)+1/9 cos(3x+4))+C

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integral of-2xcos(3x+4)

\int - 2 x cos (3 x + 4) d x

- 2 (\frac{1}{3} x sin (3 x + 4) + \frac{1}{9} cos (3 x + 4)) + C

Solution steps

\int - 2 x cos (3 x + 4) d x

Take the constant out:

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

= - 2 \cdot \int x cos (3 x + 4) d x

Apply Integration By Parts

: \frac{1}{3} x sin (3 x + 4) - \int \frac{1}{3} sin (3 x + 4) d x

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

\int \frac{1}{3} sin (3 x + 4) d x = - \frac{1}{9} cos (3 x + 4)

= - 2 (\frac{1}{3} x sin (3 x + 4) - (- \frac{1}{9} cos (3 x + 4)))

Simplify

= - 2 (\frac{1}{3} x sin (3 x + 4) + \frac{1}{9} cos (3 x + 4))

Add a constant to the solution

= - 2 (\frac{1}{3} x sin (3 x + 4) + \frac{1}{9} cos (3 x + 4)) + C

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What is the integral of-2xcos(3x+4) ?
The integral of-2xcos(3x+4) is -2(1/3 xsin(3x+4)+1/9 cos(3x+4))+C