What is the integral of 3tsin(t) ?

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

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integral of 3tsin(t)

\int 3 t sin (t) d t

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

Solution steps

\int 3 t sin (t) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int t sin (t) d t

Apply Integration By Parts

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

= 3 (- t cos (t) - \int - cos (t) d t)

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

= 3 (- t cos (t) - (- sin (t)))

Simplify

= 3 (- t cos (t) + sin (t))

Add a constant to the solution

= 3 (- t cos (t) + sin (t)) + C

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