How Do You Solve the Integral of e^x * sqrt(1+e^x) dx?

[jimen113]

Homework Statement

Integral e$$^{}x$$$$\sqrt{}1+e^{}x$$ dx

Homework Equations

using the formula: integral e^x dx:e^x+C

The Attempt at a Solution

I tried basic substitution:
making u=sqrt 1+e^x, and when trying to find du I'm not sure on what to do next

 

[Dick]

Just try u=(1+e^x). I think you'll find it goes more simply.

 

[HallsofIvy]

Homework Statement

Integral e$$^{}x$$$$\sqrt{}1+e^{}x$$ dx

Do you mean
$$\int e^x\sqrt{1+ e^x}dx$$

If so just u= 1+ e^x is sufficient.

(Put your "x" inside the "{ }" in tex!

Homework Equations

using the formula: integral e^x dx:e^x+C

The Attempt at a Solution

I tried basic substitution:
making u=sqrt 1+e^x, and when trying to find du I'm not sure on what to do next[/QUOTE]

 

[jimen113]

thanks!

 

[jimen113]

Solved:
2/3 sqrt(1+e^x)^3