Weird vector projection form

Question

Let $C^0[1,3]$ be the $\Bbb R$-vector space equipped with the usual scalar product (by the integral ). Calculate the projection of the function $f(x)= 1/x$ onto the subspace $W = L\{x\}$

Well, my solution was take $L\{x\}$ as the vector space and then do a projection of the $1/x$ on to $x$ vector space of which I ended with a single digit number of $2$ but still unsure seems an arithmetic mistake or something.

Answer 1

The projection of $u$ on the space spanned by $v$ is $v(u.v)/(v.v)$. In this case, it is $$\frac{x\int_1^3 (x)(1/x)dx}{\int_1^3(x)(x)dx}$$