What is the integral of 2xsin(6x) ?

The integral of 2xsin(6x) is 2(-1/6 xcos(6x)+1/36 sin(6x))+C

integral of 2xsin(6x)

\int 2 x sin (6 x) d x

2 (- \frac{1}{6} x cos (6 x) + \frac{1}{36} sin (6 x)) + C

Solution steps

\int 2 x sin (6 x) 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 (6 x) d x

Apply Integration By Parts

= 2 (- \frac{1}{6} x cos (6 x) - \int - \frac{1}{6} cos (6 x) d x)

\int - \frac{1}{6} cos (6 x) d x = - \frac{1}{36} sin (6 x)

= 2 (- \frac{1}{6} x cos (6 x) - (- \frac{1}{36} sin (6 x)))

Simplify

= 2 (- \frac{1}{6} x cos (6 x) + \frac{1}{36} sin (6 x))

Add a constant to the solution

= 2 (- \frac{1}{6} x cos (6 x) + \frac{1}{36} sin (6 x)) + C

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What is the integral of 2xsin(6x) ?
The integral of 2xsin(6x) is 2(-1/6 xcos(6x)+1/36 sin(6x))+C