What is the integral of 2tcos(t) ?

The integral of 2tcos(t) is 2(tsin(t)+cos(t))+C

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integral of 2tcos(t)

\int 2 t cos (t) d t

2 (t sin (t) + cos (t)) + C

Solution steps

\int 2 t cos (t) d t

Take the constant out:

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

= 2 \cdot \int t cos (t) d t

Apply Integration By Parts

= 2 (t sin (t) - \int sin (t) d t)

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

= 2 (t sin (t) - (- cos (t)))

Simplify

= 2 (t sin (t) + cos (t))

Add a constant to the solution

= 2 (t sin (t) + cos (t)) + C

What is the integral of 2tcos(t) ?
The integral of 2tcos(t) is 2(tsin(t)+cos(t))+C