# Integral Cake Delivery IIIIII

Calculus Level 4

$\large \int_1^e \dfrac{\sqrt[3]{x} }{ x (\sqrt x + \sqrt[3]{x} )} \, dx$

If the value of the integral above is equal to $a- b \ln(c+ \sqrt[d]{e} ) + f \ln g,$

where $$a,b,c,d,f$$ and $$g$$ are positive integers with $$b$$ and $$g$$ minimized, find $$a+b+c+d+f+g$$.

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