\[\large \int_{1}^{\infty} \dfrac {2x\{x\} - \{x\}^2} {x^2 \lfloor x \rfloor ^2} \, dx \]

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.

×

Problem Loading...

Note Loading...

Set Loading...