help rewriting an integral

hey...so my problem is to rewrite the [integral from 0 to pi/2] of $\displaystyle SQRT(1 + (asinx)^2)dx $in terms of the elliptic integral E(k, phi) = [integral from 0 to phi] $\displaystyle SQRT(1-(ksinu)^2)du$.

please note i am aware elliptic integrals are unsolvable in closed form...i am not looking for a solution, I am just attempting to rewrite the integral to make it look like the form of the elliptic integral E

using the substitution tanu = asinx, I have worked it out to be: [integral from 0 to arctan(asinx)] $\displaystyle du/((cosu)^2*SQRT(a^2 - (a^2 + 1)(sinu)^2))$

but I can't figure out where to go from here. Please help!