Length of Curve $6xy=3+x^4$ Question :

Find the length of the curve $6xy=3+x^4$ between $x=1$ and $x=2$.
Answer = 17/12 

I have tried this:


I obtain a different answer. Where did I do wrongly?
Thank you for your help.

Your integration is not correct.  You should simplify the integrand before proceeding.  We have $$\mathscr{L}=\int_{1}^{2}\sqrt{1+\left(\frac{x^{4}-1}{2x^2}\right)^{2}}dx=\int_{1}^{2}\sqrt{\frac{(x^{4}+1)^2}{4x^4}}dx\\=\int_{1}^{2}\frac{x^{4}+1}{2x^2}dx=\frac{1}{2}\int_{1}^{2} x^2\,dx+\frac{1}{2}\int_{1}^{2} \frac{1}{x^2}dx\\=\frac{1}{6}x^3\biggr|_{1}^{2}-\frac{1}{2}\frac{1}{x}\biggr|_{1}^{2}=\frac{17}{12}$$
