# My favourite number

**Calculus**Level 5

Given that \[I=\displaystyle\int \limits^{\infty }_{0}\left( \dfrac{1-\cos ( \sqrt[3]{42} x) }{x^{2}} \right) ^{2}\, dx= A\pi.\] Find \(A\).

**Bonus**
Find the closed form of
\[\displaystyle\int \limits^{\infty }_{0}\left( \dfrac{1-\cos ( \alpha x) }{x^{2}} \right) ^{2}\, dx \]