Should that be y prime = 1 + the rest?

Though, I'm getting y prime = 1 - the rest. Anyway, just in case a picture helps...

... where...

... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x. The right-hand differentiation uses the FTC.

Edit: here's a neater pic...

Then, writing the lower integral as the solution for the top one in the top row...

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!