What is the integral of tsin(3t) ?

The integral of tsin(3t) is -1/3 tcos(3t)+1/9 sin(3t)+C

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integral of tsin(3t)

\int t sin (3 t) d t

- \frac{1}{3} t cos (3 t) + \frac{1}{9} sin (3 t) + C

Solution steps

\int t sin (3 t) d t

Apply Integration By Parts

: - \frac{1}{3} t cos (3 t) - \int - \frac{1}{3} cos (3 t) d t

= - \frac{1}{3} t cos (3 t) - \int - \frac{1}{3} cos (3 t) d t

\int - \frac{1}{3} cos (3 t) d t = - \frac{1}{9} sin (3 t)

= - \frac{1}{3} t cos (3 t) - (- \frac{1}{9} sin (3 t))

Simplify

= - \frac{1}{3} t cos (3 t) + \frac{1}{9} sin (3 t)

Add a constant to the solution

= - \frac{1}{3} t cos (3 t) + \frac{1}{9} sin (3 t) + C

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What is the integral of tsin(3t) ?
The integral of tsin(3t) is -1/3 tcos(3t)+1/9 sin(3t)+C