If, $A=\int _{ 0 }^{ 1 }{ \left( \sum _{ i=0 }^{ 2014 }{ { x }^{ i } } \right) dx } -\int _{ 0 }^{ \infty }{ \left( \frac { { e }^{ -t }-{ e }^{ -2t }-t{ e }^{ -2016 } }{ t-t{ e }^{ -t } } \right) dt }$

Find: $\\ \left\lfloor 10000A \right\rfloor$

The answer is 5772.

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$\large{\psi \left( s+1 \right) =-\gamma +\displaystyle\int _{ 0 }^{ 1 }{ \frac { 1-{ x }^{ s } }{ 1-x } } dx\\ \\ \psi \left( s \right) =\displaystyle \int _{ 0 }^{ \infty }{ \left( \frac { { e }^{ -t } }{ t } -\frac { { e }^{ -st } }{ 1-{ e }^{ -t } } \right) } dt}$

where $\gamma$ is $\text{Euler Mascheroni constant}$ and its value is equal to $0.5772156$ .

$\large{A=\gamma}$