SimPly InteGrate It !!!

Calculus Level 5

If \(\alpha\) = \(\displaystyle \int_{0}^{1}(\prod _{r=1}^{2015}(x+r))\cdot (\sum_{k=1}^{2015}(\dfrac{1}{x+k})) \mathrm dx \)

Then \(\alpha\) can be expressed as \(A!B\).

Find \(\dfrac{A+B}{25} + \dfrac{9,573}{A+B+\dfrac{A}{5}-212}\).

\(\bullet \textbf{Details}\)

Answer Upto 3 Decimal Places

\(A,B\) Both Are \(\textbf{4 Digits Numbers}\)

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