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

Exercise

Evaluate the integral

∫0∞e−3x+e−6xe−2x+e−xdx\int_{0}^{\infty} \frac{e^{-3x}+e^{-6x}}{e^{-2x}+e{-x}} dx

Final Answer


∫0∞e−3x+e−6xe−2x+e−xdx=512\int_{0}^{\infty}\frac{e^{-3x}+e^{-6x}}{e^{-2x}+e{-x}} dx=\frac{5}{12}

Solution

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