Interactive Mathematics by Kunio Mitsuma, Ph.D.

Then, we wonder what we should have on the right-hand side.

(1) The exponent must be raised by 1. So, we first look at

(2) If this was part of the answer, then we should differentiate it and see if we could recover the original integrand. The differentiation yields

(3) The 3x² was not present in the original integrand. And, we cannot just divide the expression in (1) by 3x², because it would create the monster

whose derivative would be nowhere close to the original integrand.

From (1)–(3), we conclude that we cannot determine the given indefinite integral using basic algebra and the derivative formulas.