What is the integral of (sin(t)+cos(t)t) ?

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

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integral of (sin(t)+cos(t)t)

\int (sin (t) + cos (t) t) d t

t sin (t) + C

Solution steps

\int sin (t) + cos (t) t d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Simplify

= t sin (t)

Add a constant to the solution

= t sin (t) + C

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