# Integral with e^x need help

1. Sep 4, 2014

### Michael Gulley

The problem I have is

∫(2e^x)/(e^x+e^-x)dx

I cannot seem to get to the correct result, ln(e^2x + 1). I always have (e^2x)ln(e^2x + 1). What do I need to do, to get rid of the e^2x.
Any help would be greatly appreciated.

2. Sep 4, 2014

### vela

Staff Emeritus
Do the problem correctly. How's that for a nice vague reply? Unfortunately, that's about all anyone can say without seeing your work. How are we supposed to see where you're going wrong if you don't show your work?

3. Sep 4, 2014

### END

Step 1. Try to simplify the problem (i.e., take any constants out of the integral).

Step 2. You may want to try u-substitution.

4. Sep 4, 2014

### jz92wjaz

Hint: What's the derivative of e^2x?

I think this is probably where the mistake was made.

5. Sep 6, 2014

### parthj09

Its simple. Multiply your numerator and denominator by e^x. This will get you (2e^2x)/(e^2x + 1)dx. Now suppose your whole denominator as another variable,say, t. Calculate dt which will be equal to 2e^2xdx.
So now your integral is in the form of (1/t)dt. Integration of this will give you ln(t). Substitute back the value of 't' and there you have it.