9.4.14 Curvilinear integrals

(3) Problem: Having checked that the integrand is a total differential, calculate the line integral of the \( 2^{\text {nd }} \) kind. \[ \int_{(0,0)}^{(1,1)} x\left(1+6 y^{2}\right) d x+y\left(1+6 x^{2}\right) d y \]