Just in case you don't have this picture in your notes...
... where
... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the present variable (x or theta), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).
The general drift...
Spoiler:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!