# Improper Integral – A sum of exponential functions on an infinite interval – Exercise 6989

Exercise

Evaluate the integral

$$\int_{0}^{\infty}[{(\frac{1}{2})}^x+{(\frac{1}{3})}^x]dx$$

$$\int_{0}^{\infty}[{(\frac{1}{2})}^x+{(\frac{1}{3})}^x]dx=\frac{1}{\ln 2}+\frac{1}{\ln 3}$$