Hello! Permissible is probably the wrong word, but here's what I am having difficulty with: With substitutions in integration to make the integral easier to solve, there doesn't seem to be a restriction on the substitution one can use with indefinite integration. If one function, or part of a function, is replaced with a different function of a different variable, e.g. [tex]\sqrt(3-4/5x)[/tex], where sin(y) = 4/5x, as a random example, and they have different ranges for values, this doesn't seem to matter: You can replace one function with another, solve the integral, and convert back. There is one anti derivative for the function, so if you convert back, whereas it might have worked for a limited range of values for a definite integral with the substitution, in the indefinite form, once converted back, can work for all values. Does that make any sense? It seems to me any substitution can be made, the integral solved, and then convert back to the original variable. This can't be true, because when reading about subsitutions to solve integrals the range of values is important to consider. I hope this makes sense, Any help appreciated.