Solve with integrating an implicit function

[Helge Gabert]

Thank you very much, Bernard, this works!

May I ask three questions?

Step 1: why does this only work with fsolve and not with nSolve (here, the Prime hangs)? - - by the way, the index on the Prime needs to be 1, not 0 - 0 is the convention in Xcas for the first element of a vector, I assume.

Step 2: why does this only work with romberg, but not with int? - - also, by the way, - 1/3 needs to be appended to the integral in step two, otherwise there will be no opposite signs in step 3, and then, in step 4, h(t): will be simply t-g(t)/f(t).

Step 4: why does one have to resort to an explicit Newton construct to find the root, and cannot use fsolve again?

[P.S. Figured out why romberg works - - because it returns the numerical result right away - - so only two questions left!]