Solution
= Solution
For fixed $x\ne0$, the <chain rule> and the derivative of the <hyperbolic secant> give
$$
\frac{\partial}{\partial y}\left[-\frac1x\operatorname{sech}(xy)\right]=\operatorname{sech}(xy)\tanh(xy).
$$
Thus the stated antiderivative holds, with its integration constant independent of $y$ but allowed to depend on $x$. At $x=0$ the integrand is zero and the antiderivative is simply constant; the displayed formula with $1/x$ is meant for nonzero $x$.