Integral with e^x: Solving for ln(e^2x + 1)

[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.

 

[vela]

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?

 

[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.

 

[jz92wjaz]

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

I think this is probably where the mistake was made.

 

[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.