\[ \int \frac {(a-b x)^{3/2}}{x^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {2 \left (-b x +a \right )^{\frac {3}{2}}}{3 x^{\frac {3}{2}}}+2 b^{\frac {3}{2}} \arctan \left (\frac {\sqrt {b}\, \sqrt {x}}{\sqrt {-b x +a}}\right )+\frac {2 b \sqrt {-b x +a}}{\sqrt {x}} \]
command
int((-b*x+a)^(3/2)/x^(5/2),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(-\frac {2 \sqrt {-b x +a}\, \left (-4 b x +a \right )}{3 x^{\frac {3}{2}}}+\frac {b^{\frac {3}{2}} \arctan \left (\frac {\sqrt {b}\, \left (x -\frac {a}{2 b}\right )}{\sqrt {-x^{2} b +a x}}\right ) \sqrt {x \left (-b x +a \right )}}{\sqrt {x}\, \sqrt {-b x +a}}\) | \(71\) |
Maple 2021.1 output
\[ \int \frac {\left (-b x +a \right )^{\frac {3}{2}}}{x^{\frac {5}{2}}}\, dx \]________________________________________________________________________________________