What is the integral of (tcos(t)) ?

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

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integral of (tcos(t))

\int (t cos (t)) d t

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

Solution steps

\int t cos (t) d t

Apply Integration By Parts

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

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

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

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

Simplify

= t sin (t) + cos (t)

Add a constant to the solution

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

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