Fine so far, except you're missing a plus sign in the last line, which I assume is a typo. Now to substitute, which is really in order to work backwards through the chain rule.

Just in case a picture helps...

... where (key in first spoiler) ...

Spoiler:

Spoiler:

Hope this helps - if not, someone will probably show the sub with differentials. However, I say...

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!