9.1 Problem number 59

$$\int \frac{{(a+b\text{sech}(c+d\sqrt{x}))}^2}{\sqrt{x}}dx$$

Optimal antiderivative $$\frac{4ab\arctan \left(\sinh (c+d\sqrt{x})\right)}{d}+2a^2\sqrt{x}+\frac{2b^2\tanh (c+d\sqrt{x})}{d}$$

command

int((a+b*sech(c+d*x^(1/2)))^2/x^(1/2),x)

Maple 2022.1 output

$$\int \frac{{(a+b\mathrm{sech}(c+d\sqrt{x}))}^2}{\sqrt{x}}dx$$

Maple 2021.1 output

$$2a^2\sqrt{x}+\frac{2b^2\tanh (c+d\sqrt{x})}{d}+\frac{8ab\arctan \left({\mathrm{e}}^{c+d\sqrt{x}}\right)}{d}+\frac{2a^{2}c}{d}$$