What is the integral of sin(x+2) ?

The integral of sin(x+2) is -cos(x+2)+C

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integral of sin(x+2)

\int sin (x + 2) d x

- cos (x + 2) + C

Solution steps

\int sin (x + 2) d x

Apply Integration By Parts

: sin (x + 2) x - \int cos (x + 2) x d x

= sin (x + 2) x - \int cos (x + 2) x d x

\int cos (x + 2) x d x = x sin (x + 2) + cos (x + 2)

= sin (x + 2) x - (x sin (x + 2) + cos (x + 2))

Simplify

sin (x + 2) x - (x sin (x + 2) + cos (x + 2)) : - cos (x + 2)

= - cos (x + 2)

Add a constant to the solution

= - cos (x + 2) + C

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