# Let's integrate 2

Calculus Level 2

$\displaystyle \int \dfrac{x^3}{\sqrt[3]{1+x^4}} dx$

If the value of above expression is in the form $$\frac{A}{B}\sqrt[X]{(1+x^4)^{Y}}+C$$, where $$A,B,X,Y$$ are positive integers with $$\gcd(A,B) = \gcd(X,Y) = 1$$, find $$A+B+X+Y$$.

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