What is the integral of e^xcos(e^x+2) ?

The integral of e^xcos(e^x+2) is sin(e^x+2)+C

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integral of e^xcos(e^x+2)

\int e^{x} cos (e^{x} + 2) d x

sin (e^{x} + 2) + C

Solution steps

\int e^{x} cos (e^{x} + 2) d x

Apply u-substitution

: \int cos (u) d u

= \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= sin (u)

Substitute back

u = e^{x} + 2

= sin (e^{x} + 2)

Add a constant to the solution

= sin (e^{x} + 2) + C

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What is the integral of e^xcos(e^x+2) ?
The integral of e^xcos(e^x+2) is sin(e^x+2)+C