Analyse the integrals to tell which can be expressed in elementary functions. The two integrals are $$\frac {x}{\sqrt {x^4+10x^2-96x-71}},\frac {x}{\sqrt {x^4+10x^2-96x-72}} $$. I just typed (hardest integrals to solve) and these intgrals were in one of the answers on quora. So I am just wondering if there is some kind of algorithm or analysis we can use to show which can expressed in elemantary functions and which not. I dont want exact antiderivatives just yes or no with a proof! Thanks!
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Bleh, anti-derivatives? I prefer bounds to work with ;P – Simply Beautiful Art May 31 '17 at 17:13
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2This may help. – Simply Beautiful Art May 31 '17 at 17:14
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@ Simply beautiful art that is a good answer but the square root in denominator is kind of irritating can you tell me what can we do there? – Archis Welankar May 31 '17 at 17:16
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the first integral leads to an elliptic function, the second one also – Dr. Sonnhard Graubner May 31 '17 at 17:19