>>11304640First I would let y = a*t so the bounds would be [0,1] and you can remove the dependence on a and just have a factor of 1/a^2 out front.
After that you can let t=sqrt(2)*sinh(u) to get rid of the square root in the denominator.
After these two substitutions, you should be integrating (1/a^2)/(1+2sinh(u)^2) from 0 to arcsinh(1)
This simplifies to integrating (1/a^2)/cosh(2u) from 0 to arcsinh(1).
The final result should be (1/a^2)*(1/2)*arctan(sinh(2*arcsinh(1)))
