## How to integrate a fraction of sums of exponentials?

Is it possible to have an solution to this sort of integral? And if not, why not?

$$\int_0^\infty \frac{e^{-ax}}{e^{-bx}+e^{-cx}}dx$$

Is a Taylor expansion the only way forward?

Many thanks
David
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 Quote by DRJP Is it possible to have an solution to this sort of integral? And if not, why not? $\int_0^\infty \frac{e^{-ax}}{e^{-bx}+e^{-cx}}dx$ Is a Taylor expansion the only way forward? Many thanks David
$$\int_0^\infty \frac{e^{-ax}}{e^{-bx}+e^{-cx}}dx$$
Then try to get rid of as many exponentials as possible. You can make the substitution (a,b,c >0) $\displaystyle{e^{-ax}} = t$ and see what you get.