How to integrate a fraction of sums of exponentials?by DRJP Tags: exponentials, fraction, integrate, sums 

#1
Dec2111, 07:20 AM

P: 1

Is it possible to have an solution to this sort of integral? And if not, why not?
[tex] \int_0^\infty \frac{e^{ax}}{e^{bx}+e^{cx}}dx [/tex] Is a Taylor expansion the only way forward? Many thanks David 



#2
Dec2111, 07:29 AM

Sci Advisor
HW Helper
P: 11,863

[tex]\int_0^\infty \frac{e^{ax}}{e^{bx}+e^{cx}}dx[/tex] looks better and is easier to read. As for your question, before jumping to series expansions and substitutions, specify if the arbitrary constants are positive or negative. This makes a huge difference on the final result. Then try to get rid of as many exponentials as possible. You can make the substitution (a,b,c >0) [itex] \displaystyle{e^{ax}} = t [/itex] and see what you get. 


Register to reply 
Related Discussions  
Partial Sums resembling sums of secant hyperbolic  Calculus & Beyond Homework  0  
Statistical mechanics: Sums of exponentials with sums.  Advanced Physics Homework  3  
How to integrate this fraction function  help  Calculus & Beyond Homework  5  
(revised+repost)Upper and Lower sums & Riemann sums  Calculus & Beyond Homework  3  
Sequences, Cumulative Sums, Partial Sums Plot  Ti89 Titanium  Calculators  0 