# Look familiar? (My seventeenth integral problem)

Calculus Level 5

$\large \displaystyle \int_{0}^{1} \dfrac{1-x^{3}}{1+x^{3}} \, dx$

If the above integral can be expressed in the form

$-a + \dfrac{b \pi \sqrt{c}}{d} + \dfrac{f\ln 2}{g}$

where $$a, b, c, d, f, g$$ are positive integers and $$\gcd(b, d)=\gcd(f, g)= 1$$, find $$a+b+c+d+f+g$$.

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