# Differentiate to integrate, SImple

Calculus Level 5

$\large{\displaystyle \int^{\infty}_{0} \frac{1}{6x^3+7} \left( \frac { { d }^{ \frac { 1 }{ 2 } }x }{ d{ x }^{ \frac { 1 }{ 2 } } } \right) dx}$

The value of above expression equals $$\large{\frac{\pi^{A}}{B^{C}D^{E}F^{G}}}$$

for prime numbers $$B,D,F$$ and $$A,C,E,G\in \mathbb R$$

Find $$A+B+C+D+E+F+G$$.

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