What is the integral of t*sin(t) ?

The integral of t*sin(t) is -tcos(t)+sin(t)+C

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integral of t*sin(t)

\int t \cdot sin (t) d t

- t cos (t) + sin (t) + C

Solution steps

\int t sin (t) d t

Apply Integration By Parts

: - t cos (t) - \int - cos (t) d t

= - t cos (t) - \int - cos (t) d t

\int - cos (t) d t = - sin (t)

= - t cos (t) - (- sin (t))

Simplify

= - t cos (t) + sin (t)

Add a constant to the solution

= - t cos (t) + sin (t) + C

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What is the integral of t*sin(t) ?
The integral of t*sin(t) is -tcos(t)+sin(t)+C