1. integral help

ok, so i have to integrate (e^x-e^-x)/(e^x+e^-x). any ideas on how to solve this problem?

2. Let $\displaystyle {\color{red}u = e^x + e^{-x}} \ \Rightarrow \ {\color{blue}du = \left(e^x - e^{-x} \right)dx}$

So your integral becomes: $\displaystyle \int \frac{{\color{blue}e^x-e^{-x}}}{{\color{red}e^x + e^{-x}}} \ {\color{blue} dx} = \cdots$

3. Put the bottom equal to u. Take its derivative. It's going to equal the top. You will thus conclude that it is ln(denominator)

4. ok, kewl. i see wat i did wrong now. i differentiated e^-x wrong. forgot that it was negative. thanks guys, really appreciate it.

5. Originally Posted by needhelp101
ok, so i have to integrate (e^x-e^-x)/(e^x+e^-x). any ideas on how to solve this problem?
Or, you might recognise the definition of a familiar hyperbolic function and hence a standard integral ....

6. solution of the integral

Your (E^x-E^(-x))/(E^x+E^(-x)) equals Tanh[x]. And its integral is Ln[Cosh[x]]. Please visit one of most powerful math engines:
http://integrals.wolfram.com/index.jsp
All the best. Marek.