What is the integral of xsin(11x) ?

The integral of xsin(11x) is -1/11 xcos(11x)+1/121 sin(11x)+C

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integral of xsin(11x)

\int x sin (11 x) d x

- \frac{1}{11} x cos (11 x) + \frac{1}{121} sin (11 x) + C

Solution steps

\int x sin (11 x) d x

Apply Integration By Parts

: - \frac{1}{11} x cos (11 x) - \int - \frac{1}{11} cos (11 x) d x

= - \frac{1}{11} x cos (11 x) - \int - \frac{1}{11} cos (11 x) d x

\int - \frac{1}{11} cos (11 x) d x = - \frac{1}{121} sin (11 x)

= - \frac{1}{11} x cos (11 x) - (- \frac{1}{121} sin (11 x))

Simplify

= - \frac{1}{11} x cos (11 x) + \frac{1}{121} sin (11 x)

Add a constant to the solution

= - \frac{1}{11} x cos (11 x) + \frac{1}{121} sin (11 x) + C

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What is the integral of xsin(11x) ?
The integral of xsin(11x) is -1/11 xcos(11x)+1/121 sin(11x)+C