Belles intégrales

Calculus Level 5

\[ \large \begin{align} \int_{1}^{\infty} \frac{\{x\}}{x^3} dx & =a-\frac{{\pi}^2}{b} \\ \int_{1}^{\infty} \frac{\{x\}-\frac{1}{2}}{x} dx & = \ln(\sqrt{c\pi})-d \end{align} \]

Integers \(a\), \(b\), \(c\) and \(d\) satisfy the respective equations above. Find \(\sqrt{a+b+c+d}\).

Notation: \( \{ \cdot \} \) denotes the fractional part function.

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