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# An interesting integral

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Evaluate the following integral

$$\int {\sqrt{4+\sqrt{4+\sqrt{4+\dots +\sqrt{4+x}}}} dx}$$

Aug 18, 2021

#1
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Like so:

Aug 18, 2021
#2
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Oh, Thank you! but I think the sequence is finite, so we can't just say what you did with y(x).

Guest Aug 19, 2021
#3
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The ellipsis (the ...) usually indicates continuation forever.  If the sequence is finite then perhaps the number of levels should be specified.

Alan  Aug 19, 2021