What is the integral of tsin(6t) ?

The integral of tsin(6t) is -1/6 tcos(6t)+1/36 sin(6t)+C

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integral of tsin(6t)

\int t sin (6 t) d t

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

Solution steps

\int t sin (6 t) d t

Apply Integration By Parts

: - \frac{1}{6} t cos (6 t) - \int - \frac{1}{6} cos (6 t) d t

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

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

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

Simplify

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

Add a constant to the solution

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

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What is the integral of tsin(6t) ?
The integral of tsin(6t) is -1/6 tcos(6t)+1/36 sin(6t)+C