Improper Integral – A quotient of exponential functions on an infinite interval – Exercise 1527

Exercise

Evaluate the integral

∫3∞e−3x9+e−3xdx\int_3^{\infty} \frac{e^{-3x}}{9+e^{-3x}} dx

Final Answer


∫3∞e−3x9+e−3xdx=−13ln⁡9+13ln⁡(9+e−9)\int_3^{\infty} \frac{e^{-3x}}{9+e^{-3x}} dx=-\frac{1}{3}\ln 9+\frac{1}{3}\ln(9+e^{-9})

Solution

Coming soon…

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