Improper Integral of ln(sinx) from 0 to pi/2: MIT Integration Bee (4) - YouTube
Evaluating the integral of ln(sin(x)) from x = 0 to x = π. : r/IntegrationTechniques
The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decreasing in (0,oo) increasing in (0,pi/e), decreasing in (pi/e ,oo) decreasing in (0, pi/e), increasing in (pi/e ,oo)
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ln|cos(pi/4)
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