## Need to solve: Int (x/(sqrt((exp(x)-a)*(b-exp(x))) dx

Limits, differentiation, related rates, integration, trig integrals, etc.

### Need to solve: Int (x/(sqrt((exp(x)-a)*(b-exp(x))) dx

Int (x/(sqrt((exp(x)-a)*(b-exp(x))) dx

In my opinion is impossible.
leotrav

Posts: 1
Joined: Wed Jul 08, 2009 9:56 am

Wolfram's online integrator could not come up with an answer when differing numbers were plugged in for "a" and "b". This suggests that your conclusion may be correct....

Note: I first used a = 1, b = 2, and entered "x/Sqrt[(Exp[x]-1)(2-Exp[x])]" in the box. When I plugged "2" in for each, The Integrator returned the following:

. . . . .$\Large{-\frac{(e^x\, -\, 2)\left(x\left(x\, -\, 2\ln\left(1\, -\, \frac{e^x}{2}\right)\right)\, -\, 2\,\mbox{Li}_2\left(\frac{e^x}{2}\right)\right)}{4\, \sqrt{-(e^x\, -\, 2)^2}}}$

...where "Li2" is something called the "polylog function"...?

stapel_eliz

Posts: 1784
Joined: Mon Dec 08, 2008 4:22 pm