Length of a curve

$$ Length of curve is $$ $\begin{aligned} L&=\int_0^9 \sqrt{1+\left(\frac{dy}{dx}\right)^2} \,dx\\ &=\int_0^9 \sqrt{1+(x\sqrt{x^2+1})^2} \,dx\\ &=\int_0^9 \sqrt{x^4+2x^2+1} \,dx\\ &=\int_0^9 \sqrt{(x^2+1)^2} \,dx\\ &=\int_0^9 (x^2+1) \,dx\\ &=\left. \frac{1}{3}x^3+x\right|_0^9\\ &=\boxed{252}. \end{aligned}$ $$ $\text{\# }\mathbb{Q}.\mathbb{E}.\mathbb{D}.\text{\#}$