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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?

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    $\begingroup$ 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))] $\endgroup$ – thorimur Mar 16 at 0:52
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    $\begingroup$ @thorimur Using Simplify on ! (x <= 0 || (! 0 < x <= 1 && x > 1)) gets one 0 < x <= 1. $\endgroup$ – JimB Mar 16 at 3:35
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    $\begingroup$ nice, yeah! i was just copy-pasting the result verbatim to show it finished 🙃 $\endgroup$ – thorimur Mar 16 at 3:54
  • $\begingroup$ Include assumptions: Assuming[a >= 0 && 0 <= x <= 1, Integrate[E^(a*InverseCDF[NormalDistribution[0, 1], (1 - x)]), x]] $\endgroup$ – Bob Hanlon Mar 16 at 4:51

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