\[ \int \frac {\sqrt {a-b x}}{x^{3/2}} \, dx \]
Optimal antiderivative \[ -2 \arctan \left (\frac {\sqrt {b}\, \sqrt {x}}{\sqrt {-b x +a}}\right ) \sqrt {b}-\frac {2 \sqrt {-b x +a}}{\sqrt {x}} \]
command
int((-b*x+a)^(1/2)/x^(3/2),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(-\frac {2 \sqrt {-b x +a}}{\sqrt {x}}-\frac {\sqrt {b}\, \arctan \left (\frac {\sqrt {b}\, \left (x -\frac {a}{2 b}\right )}{\sqrt {-x^{2} b +a x}}\right ) \sqrt {x \left (-b x +a \right )}}{\sqrt {x}\, \sqrt {-b x +a}}\) | \(66\) |
Maple 2021.1 output
\[ \int \frac {\sqrt {-b x +a}}{x^{\frac {3}{2}}}\, dx \]________________________________________________________________________________________