I have tried many hours on the following integrals and would appreciate any help from you.
1. Int{x=0 to infinity}(exp(-x)*Ln(x)*Ln(x)dx)
2. Int{x=0 to Infinity}(exp(-x*x)*Ln(x)dx)
Any idea guys?
Hi guys,recently I came across the following integral and need assistance in solving the problem.
The crux of the problem is calculating the definite integral of log(sin(x)*sin(x)) over
the interval ( 0, Pi/2).
Sorry, I made a mistake in typing the integrand.
It should be (Log(sin(x)))^2 instead.
guys,
From the solutions of the Pell's equation x*x-2*y*y=-1,
how can we prove that whenever y ends in digit 5, then 7 | x ?
-Mathslover
Perhaps I should clarify a bit,x*x-2*y*y=-1 has solution
x=1, 7, 41, 239, 1393, 8119, 47321, 275807,.....
y=1, 5, 29, 169, 985, 5741, 33461, 167305...