integral help

**needhelp101** · January 21st 2009, 04:05 PM

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

**o_O** · January 21st 2009, 04:08 PM

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

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

**vincisonfire** · January 21st 2009, 04:08 PM

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)

**needhelp101** · January 21st 2009, 04:10 PM

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

**mr fantastic** · January 22nd 2009, 01:16 AM

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 ....

**marek** · January 22nd 2009, 01:40 AM

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.

Thread: integral help

LinkBack

Thread Tools

Display

integral help

solution of the integral

Similar Math Help Forum Discussions

Use Cauchy's integral theorem for derivatives to evaluate the contour integral.

Graph the region of integration and evaluate the double integral (integral from 0 to

Explaining result: comparing line integral and two-form integral

write [integral of] dx/SQRT(sinx) in terms of an elliptic integral

Evaluating a double integral to find its signle integral.

Search Tags