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Neat. And if you multiply the top and bottom of the original integrand by exp(-x), you'll be left to integrate [exp(-x)/(exp(-1) + 1)], from 0 to infinity, which results in -ln( exp(-x) + 1) from 0 to infinity which gives -ln(1) + ln(2) = ln 2
as far as i know it goes to ln(2)
That is correct. The integral converges to ln(2).
@calculusproblemsandsolutio7914 i used desmos to calculate it but i wanted to say it since this popped up on my recommended
Neat. And if you multiply the top and bottom of the original integrand by exp(-x), you'll be left to integrate [exp(-x)/(exp(-1) + 1)], from 0 to infinity, which results in -ln( exp(-x) + 1) from 0 to infinity which gives -ln(1) + ln(2) = ln 2
as far as i know it goes to ln(2)
That is correct. The integral converges to ln(2).
@calculusproblemsandsolutio7914 i used desmos to calculate it but i wanted to say it since this popped up on my recommended