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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

Final Answer


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

Solution

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