What is the integral of vsin(v) ?

The integral of vsin(v) is -vcos(v)+sin(v)+C

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integral of vsin(v)

\int v sin (v) d v

- v cos (v) + sin (v) + C

Solution steps

\int v sin (v) d v

Apply Integration By Parts

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

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

= - v cos (v) - (- sin (v))

Simplify

= - v cos (v) + sin (v)

Add a constant to the solution

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