I have been trying to do this question and I keep getting $\displaystyle v_3$ different to what my lecturer has in the notes. Can anyone please find $\displaystyle v_1$, $\displaystyle v_2$ and $\displaystyle v_3$ for me?!

The question is:

The equations used in the process are hereApply the Gram-Schmidt orthogonalization procedure to the R-basis $\displaystyle \{{1, x, x^2, x^3}\}$ to obtain an orthonormal basis for $\displaystyle P_3(R)$ where the inner product is defined by

$\displaystyle \int_{-1}^{1} (1-x^2)f(x)g(x) \, dx$

I dont need the working out, I just want to know the final answers for $\displaystyle v_1$, $\displaystyle v_2$ and $\displaystyle v_3$. Thank you!