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  1. M

    Two Integrals

    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?
  2. M

    Summation involving von Mangoldt function

    Please help me in solving the problem, find the sum Sum{r=2 to infinity} (von Mangoldt(r)-1)/r Your help is appreciated.
  3. M

    Strange Incredible Identity

    How can we proceed to prove the following identity ?
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    A Difficult Integral

    How should we proceed to find the definite integral Int[ log(sin(x))*log(cos(x)) ,{x,0,pi/2} ] ? mathslover
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    Integral Calculation

    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.
  6. M

    Pell's equation 5 and 7

    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...