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How does one go about integrating:

$\int\sqrt{a + x^3}dx$

Wolframalpha seems to be giving a result that seems slightly too elaborate.

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    For $a\ne 0$, there probably is no antiderivative expressible in terms of "elementary" functions. Presumably Alpha used elliptic functions in its answer.2012-12-03

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why not use u-substitution? u = a+x^3 then du=3x^2 dx. Should be a good start.

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    Well, it doesn't look very promising, does it? Just take into account that $dx=\frac{1}{3x^2}du=\frac{du}{3(u-a)^{2/3}}\,...$2012-12-03