Derivative and Integral of two Infinitely Nested Radicals - Inspired by MIT Integration Bee

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In this video, we go over how one might find how to find the derivatives of two infinitely nested radicals. The basic idea is to convert the infinitely nested radical into a closed form algebraic expression, then integrate that.
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On the second one you can write it as y=sqrt(xsqrt(xsqrt(x... then substitute y in to get y=sqrt(xy) --> y^2=xy --> y=x, int(xdx)=x^2/2

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