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## Homework Statement

[tex]\int[/tex]e[tex]^{x}[/tex][tex]\sqrt{1+e^{2 x}}[/tex]dx

## Homework Equations

Cosh x = [ e[tex]^{x}[/tex]+ e[tex]^{-x}[/tex] ] / 2

## The Attempt at a Solution

[tex]\int[/tex]e[tex]^{x}[/tex][tex]\sqrt{1+e^{2x}}[/tex]dx

= [tex]\int[/tex]e[tex]^{x}[/tex][tex]\sqrt{2e^{x}Cosh x}[/tex]dx

I have no idea on how to proceed already. I cannot obtained the solution given by Mathematica. I use substitution method by let u = e[tex]^{x}[/tex] and then use trigonometric substitution. But also no idea on how to proceed. Hoping anyone outside there can try to help me in solving this question.Thanks.

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