Int (x/(sqrt((exp(x)-a)*(b-exp(x))) dx
In my opinion is impossible.
Please help myself to rearrange in term of special function
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Need to solve: Int (x/(sqrt((exp(x)-a)*(b-exp(x))) dx 
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Need to solve: Int (x/(sqrt((exp(x)-a)*(b-exp(x))) dx
by leotrav on Wed Jul 08, 2009 9:58 am
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by stapel_eliz on Wed Jul 08, 2009 1:37 pm
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:
. . . . .\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"...?
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:
. . . . .
...where "Li2" is something called the "polylog function"...?
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stapel_eliz - Posts: 1706
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