What is the integral of e^xcosh(e^x) ?

The integral of e^xcosh(e^x) is sinh(e^x)+C

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integral of e^xcosh(e^x)

\int e^{x} cosh (e^{x}) d x

sinh (e^{x}) + C

Solution steps

\int e^{x} cosh (e^{x}) d x

Apply u-substitution

: \int cosh (u) d u

= \int cosh (u) d u

Use the common integral:

\int cosh (u) d u = sinh (u)

= sinh (u)

Substitute back

u = e^{x}

= sinh (e^{x})

Add a constant to the solution

= sinh (e^{x}) + C

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What is the integral of e^xcosh(e^x) ?
The integral of e^xcosh(e^x) is sinh(e^x)+C