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

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

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integral of sin(2+x)

\int sin (2 + x) d x

- cos (2 + x) + C

Solution steps

\int sin (2 + x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

= - cos (2 + x)

Add a constant to the solution

= - cos (2 + x) + C

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