# $$\displaystyle{x^2}$$ Laid Down On The Floor

Calculus Level 5

$\large \int_{1}^{2} \left(x^{\lfloor x^2 \rfloor} + {\lfloor x^2 \rfloor}^{x} \right) \, dx$

The integral above can be expressed as$\dfrac{a}{b} + \sqrt{c} + \dfrac{\sqrt{d}}{e} + \dfrac{2^{\sqrt{f}}-2^{\sqrt{g}}}{\ln h } + \dfrac{i - 3^{\sqrt{j}}}{ \ln k}.$ What is the sum of all of these constants from $$\displaystyle{a}$$ to $$\displaystyle{k}?$$

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