Hint: .
Just in case a picture helps...
As people have hinted...
... i.e., notice how to differentiate wrt x. I.e. consider how to differentiate wrt t, or the corresponding balloon here, wrt the dashed balloon...
But then apply the chain rule, where (key in spoiler) ...
Spoiler:
So we get...
And notice that for this we also used...
Now for the integration... we want to travel up instead of down. Can you anti-differentiate
wrt t? I.e...
If so then you're ready to fill out the rest of this...
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!