We study the sequence $\left(u_{n}\right)_{n \in \mathbb{N}^{*}}$ defined by $$\forall n \in \mathbb{N}^{*}, \quad u_{n} = \int_{0}^{\infty} \frac{1 - (\cos t)^{n}}{t^{2}} \mathrm{~d}t$$ Show that $u_{1} = u_{2} = \frac{\pi}{2}$.
We study the sequence $\left(u_{n}\right)_{n \in \mathbb{N}^{*}}$ defined by
$$\forall n \in \mathbb{N}^{*}, \quad u_{n} = \int_{0}^{\infty} \frac{1 - (\cos t)^{n}}{t^{2}} \mathrm{~d}t$$
Show that $u_{1} = u_{2} = \frac{\pi}{2}$.