If u, v, w ∈ R n , then span(u, v + w) = span(u + v, w)

${\mathrm{End}}_{\mathrm{ℝ}\left[x\right]}\left(M\right)$ where ${\displaystyle M=\frac{\mathbb{R}\left[x\right]}{(x^2+1)}}$ is a module over the ring ${\displaystyle \mathbb{R}\left[x\right]}$

Suppose$U=\{(x,y,x+y,x-y,2x)\in F^5,x,y\in F\}$ . Find a subspace $W$of $F^5$ such that $F^5=U\oplus W$.

${\int }_1^3\frac{8x}{(2x+4)*3}dx$