# Improper Integral – A quotient of exponential functions on an infinite interval – Exercise 6999

Exercise

Evaluate the integral

$$\int_{0}^{\infty} \frac{e^{-3x}+e^{-6x}}{e^{-2x}+e{-x}} dx$$

$$\int_{0}^{\infty}\frac{e^{-3x}+e^{-6x}}{e^{-2x}+e{-x}} dx=\frac{5}{12}$$