What is the integral of (x+3)cos(x) ?

The integral of (x+3)cos(x) is sin(x)(x+3)+cos(x)+C

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integral of (x+3)cos(x)

\int (x + 3) cos (x) d x

sin (x) (x + 3) + cos (x) + C

Solution steps

\int (x + 3) cos (x) d x

Apply Integration By Parts

= sin (x) (x + 3) - \int sin (x) d x

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

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

Simplify

= sin (x) (x + 3) + cos (x)

Add a constant to the solution

= sin (x) (x + 3) + cos (x) + C

What is the integral of (x+3)cos(x) ?
The integral of (x+3)cos(x) is sin(x)(x+3)+cos(x)+C