# Summations can be easy!

Calculus Level 5

$\sum_{n=0}^{\infty}\left( \dfrac{n}{2+\int_{0}^{n} \left(18x^2+26x+9\right)\, dx}\right)= \ln\left(\dfrac{a}{b}\right)-\dfrac{c \pi }{\sqrt{d}}$

$$\text{Find:}$$ $$a+b+c+d+5$$.

Details and Assumptions:

$$\bullet$$ All the constants in the RHS are positive integers. All fractions are in reduced form (co-prime). $$d$$ is a square free integer.

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