What is the integral of xsin(12x) ?

The integral of xsin(12x) is -1/12 xcos(12x)+1/144 sin(12x)+C

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integral of xsin(12x)

\int x sin (12 x) d x

- \frac{1}{12} x cos (12 x) + \frac{1}{144} sin (12 x) + C

Solution steps

\int x sin (12 x) d x

Apply Integration By Parts

: - \frac{1}{12} x cos (12 x) - \int - \frac{1}{12} cos (12 x) d x

= - \frac{1}{12} x cos (12 x) - \int - \frac{1}{12} cos (12 x) d x

\int - \frac{1}{12} cos (12 x) d x = - \frac{1}{144} sin (12 x)

= - \frac{1}{12} x cos (12 x) - (- \frac{1}{144} sin (12 x))

Simplify

= - \frac{1}{12} x cos (12 x) + \frac{1}{144} sin (12 x)

Add a constant to the solution

= - \frac{1}{12} x cos (12 x) + \frac{1}{144} sin (12 x) + C

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What is the integral of xsin(12x) ?
The integral of xsin(12x) is -1/12 xcos(12x)+1/144 sin(12x)+C