Group relations

The table below summarises the inclusion relations between frequently used Groups

Where, up to LaTeX formatting, we have:

• $\mathbb{F}$ is a Field
• $\mathbb{R}$ is the real line
• $M_n(\mathbb{F})$ is the set of $n\times n$ matrices over $\mathbb{F}$
• $M_n(\mathbb{R})$ is the set of $n\times n$ matrices over $\mathbb{R}$
• $GL(n,\mathbb{F})$ is the General Linear Group
• $SL(n,\mathbb{F})$ is the Special Linear Group
• $U(n,\mathbb{F})$ is the Unitary Group
• $SU(n,\mathbb{F})$ is the Special Unitary Group
• $O(n)$ is the Orthogonal Group
• $SO(n)$ is the Special Orthogonal Group

What is the solution to ${\int }_{\mathbb{R}}\frac{1}{x^2}dx$?