How to compute an indefinite integral for a general parameter choice?

I am trying to compute the integral:

Integrate[E^(a*InverseCDF[NormalDistribution[0, 1], (1 - x)]), x]


for a >= 0. The computation times out unless I provide a specific numerical value for a. For example for a = 0.5, I get an output. Is there a way to get the integral expression in terms of a?

• I think just wait. I eventually got the result: ConditionalExpression[E^(a^2/2)/2 + 1/2 E^(a^2/2)Erf[a/Sqrt[2] + InverseErfc[2 - 2 x]], ! (x <= 0 || (! 0 < x <= 1 && x > 1))] – thorimur Mar 16 at 0:52
• @thorimur Using Simplify on ! (x <= 0 || (! 0 < x <= 1 && x > 1)) gets one 0 < x <= 1. – JimB Mar 16 at 3:35
• nice, yeah! i was just copy-pasting the result verbatim to show it finished 🙃 – thorimur Mar 16 at 3:54
• Include assumptions: Assuming[a >= 0 && 0 <= x <= 1, Integrate[E^(a*InverseCDF[NormalDistribution[0, 1], (1 - x)]), x]] – Bob Hanlon Mar 16 at 4:51