dx-e-2x-5e-x-

Question Number 86518 by john santu last updated on 29/Mar/20

\int \frac{dx}{e^{2 x} - {5 e}^{x}}

Commented by john santu last updated on 29/Mar/20

\Rightarrow \int \frac{dx}{e^{x} (e^{x} - 5)} = \int \frac{e^{x} dx}{e^{2 x} (e^{x} - 5)}

let t = e^{x} - 5 \Rightarrow dt = e^{x} dx

\int \frac{dt}{{(t + 5)}^{2} t} = \int \frac{A}{t + 5} dt + \int \frac{B}{{(t + 5)}^{2}} dt

+ \int \frac{C}{t} dt