What is the integral of 6tsin(t) ?

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

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integral of 6tsin(t)

\int 6 t sin (t) d t

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

Solution steps

\int 6 t sin (t) d t

Take the constant out:

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

= 6 \cdot \int t sin (t) d t

Apply Integration By Parts

= 6 (- t cos (t) - \int - cos (t) d t)

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

= 6 (- t cos (t) - (- sin (t)))

Simplify

= 6 (- t cos (t) + sin (t))

Add a constant to the solution

= 6 (- t cos (t) + sin (t)) + C

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