Some elementary functions, such as f(x) = sin(x2 ), do not have antiderivatives that are elementary functions. Joseph Liouville proved that ∫ ex/ x dx does not have an elementary antiderivative. Use this fact to prove that ∫ 1 / lnx dx does not have an elementary antiderivative
Some elementary functions, such as f(x) = sin(x2 ), do not have antiderivatives that are elementary functions. Joseph Liouville proved that ∫ ex/ x dx does not have an elementary antiderivative. Use this fact to prove that ∫ 1 / lnx dx does not have an elementary antiderivative
let for n a positive integer and c a non zero constant is non elementary since has no solution in the field of rational functions over C.
As has no elementary antiderivative thus using the cases of integral of the form where a is a non zero constant and m and n are integers.
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