Determine the value of a real constant c, given that:

     y
   ∫(ln p)*(1+p)-1 dp = g(y)
    1

and, g(e^c) + g(e^-c) = c³/12

where ln x denotes the natural logarithm of x.

I start to calculate g(y)+g(1/y) .

For g(1/y) i switch the integral p=1/t and i find

g(y)+g(1/y) = (ln(y))^2/2.

For y=e^c i find c=0.

But i feel that i make something wrong in my calculus!!

Posted by Chesca Ciprian on 2008-01-09 06:21:29