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How to integrate a fraction of sums of exponentials? 
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#1
Dec2111, 07:20 AM

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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

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P: 11,896

[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. 


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