# Evaluate the following integral. {eq}\displaystyle \int e^x \cosh x \ dx {/eq}

## Question:

Evaluate the following integral.

{eq}\displaystyle \int e^x \cosh x \ dx {/eq}

## Cosine Hyperbolic Function as Integrand:

The cosine hyperbolic function is defined as the ratio of the sum of exponential functions {eq}e^x {/eq} and {eq}e^{-x} {/eq} over the integer value {eq}2 {/eq}. The product rule of exponential expression for the simplification of the integral expression is:

{eq}e^a\cdot e^b=e^{a+b} {/eq}

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Given integral:

{eq}\displaystyle \int e^x \cosh x \ dx=?\\[2ex] {/eq}

The cosine hyperbolic function in exponential form is:

{eq}\cosh...