I don't know how to answer this questions : 1) $e^x/x, exp(exp(x))$ as no elementary primitive. 2) $1/(1+x^2)$ as no elementary primitive in $R(x)$ but have one in $C(x)$. If someone could help me i will be happy :D. Thanks !
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1Page 6 and page 10 here have a statement of the theorem and an example of how it is applied. – Stahl May 20 '17 at 08:59
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OK so basically i must show that the verify a differential equation wich has no solution right ? – May 20 '17 at 09:43
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cause i don't know how to do with $exp(exp(x))$ since $exp(x)$ is not in $C(X)$. – May 20 '17 at 10:10