Finding orthonormal basis. Is there error on textbook?

Question

The problem is finding orthonormal basis for W=span{u1=x,u2=x^2}

And as lots of people think, it is not very difficult problem

My answer is

${ \sqrt{3}x,\sqrt{80}(x^2-\frac{3}{4}x) }$

But, textbook says

$ \sqrt{3}x,\sqrt{30}(x^2-\frac{1}{2}x)$

I checked another edition of the textbook but it was same.

I use elementary linear algebra by koleman

Is there any error I have made? Because of this problem I can’t believe my answer for similar problems.

Answer 1

The book's answer isn't orthogonal: $(x,x^2-\frac12x)=\int_0^1x(x^2-\frac12x)\operatorname dx=[x^4/4-x^3/6]_0^1\neq0$.

Yours, on the other hand, appears to be correct.