# Does this telescope?

Calculus Level 5

For all $$n$$ let $$\ell_n$$ denote $$\displaystyle\int_{0}^{1} {\frac{x^n}{\sqrt{x^3+1}}}$$. Suppose that $$m = \underbrace{2014...2014}_{\text{2014 times}}$$, evaluate to 3 decimal digits the value of $$(2m-1)\ell_m + 2(m-2) \ell_{m-3}$$.

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