- #1

nicnicman

- 136

- 0

## Homework Statement

[itex]\int[/itex][itex]\frac{dx}{\sqrt{e^{x} + 1}}[/itex]

## Homework Equations

Using u-substitution

## The Attempt at a Solution

Let u = [itex]\sqrt{e^{x} + 1}[/itex] [itex]\Rightarrow[/itex] u[itex]^{2} - 1[/itex] = e[itex]^{x}[/itex]

Then, du = [itex]\frac{e^{x} dx}{2\sqrt{e^{x} + 1}}[/itex] [itex]\Rightarrow[/itex] dx = [itex]\frac{2u du}{u^{2}-1}[/itex]

So, [itex]\int[/itex][itex]\frac{dx}{\sqrt{e^{x} + 1}}[/itex] = [itex]\int[/itex][itex]\frac{2u du}{u(u^{2}-1)}[/itex]

But, I'm stuck at this point. I think I want to break it up into two simpler integrals, but I'm not sure how to do this. Any suggestions would be greatly appreciated!