\[ \int \frac {\left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2}{\sqrt {x}} \, dx \]
Optimal antiderivative \[ \frac {4 a b \arctan \! \left (\sinh \! \left (c +d \sqrt {x}\right )\right )}{d}+2 a^{2} \sqrt {x}+\frac {2 b^{2} \tanh \! \left (c +d \sqrt {x}\right )}{d} \]
command
int((a+b*sech(c+d*x^(1/2)))^2/x^(1/2),x)
Maple 2022.1 output
\[\int \frac {\left (a +b \,\mathrm {sech}\left (c +d \sqrt {x}\right )\right )^{2}}{\sqrt {x}}\, dx\]
Maple 2021.1 output
\[ 2 a^{2} \sqrt {x}+\frac {2 b^{2} \tanh \left (c +d \sqrt {x}\right )}{d}+\frac {8 a b \arctan \left ({\mathrm e}^{c +d \sqrt {x}}\right )}{d}+\frac {2 a^{2} c}{d} \]