How to solve for the missing limit (integral)

Mathcad should be able to solve your equation as you wrote it and I tend to call it a bug in the symbolic engine.

Reason for Mathcad failing is that Mathcads symbol processor seems not to be able to evaluate a definite integral with symboic limit if its in float mode. Unfortunately the symbolprocessor automatically choses float mode if just one number in the expression is written with a decimal point in its representation.

So consequently, if you rewrite your equation using integers only, Mathcad finds a symbolic solution. This solution with all its nested roots is possibly not what you want to see, so I assigned it a variable "Sol" which is then evaluated either numerically or symbolically using the "float" modifier.

Again, this is a workaround (like Alan's who evaluated the integral using symbolic variables and thus avoided the float mode, too) for a bug which should not be necessary.

As you are searching for numbers only you may also consider using a solve block instead of the symbolic solve command. The solve block requires a guess value and will only yield one specific result, not all possible. Which one depends on the guess value. Plotting the function can help finding suitable guess values (see attached sheet).

EDIT: You can evaluate the solve block symbolically (you can omit the guess value if you do so) and interestingly enough this time Mathcads symbolics find the solutions!