Partition this integral!
Calculus
Level
2
\[\large \int_{1}^{\infty} \dfrac {2x\{x\} - \{x\}^2} {x^2 \lfloor x \rfloor ^2} \, dx \]
If the integral above can be expressed as \( \dfrac{\pi^a - b} c \), where \(a,b,c\) are all positive integers, find \(a+b+c\).
Notations:
- \( \{ \cdot \} \) denotes the fractional part function.
- \( \lfloor \cdot \rfloor \) denotes the floor function.
by
subh mandal