Integral problems with roots of polynomials

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SUMMARY

The integral \(\int \left( \sqrt{x^{3}+1} + \sqrt[3]{x^{2}+2x} \right) \, dx\) cannot be expressed in terms of elementary functions. The discussion highlights that solving this integral requires advanced mathematical concepts, specifically hypergeometric and elliptic functions. Users are encouraged to utilize computational tools like Wolfram Alpha for assistance in evaluating such integrals.

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Homework Statement



How do i solve this integral ?

[tex]\int \big( \sqrt{x^{3}+1} + \sqrt[3] {x^{2}+2x} \big) \ dx[/tex]

Homework Equations





The Attempt at a Solution



what is the appropriate substitution to make here
 
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There is no antiderivative of this function that could be written down using elementary functions only. It takes some hypergeometric and elliptic functions, type it down into wolfram alpha and see what you get.
 

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