Optimal. Leaf size=23 \[ \frac{2 x^{5/2} \left (a+\frac{b}{x}\right )^{5/2}}{5 a} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0262079, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{2 x^{5/2} \left (a+\frac{b}{x}\right )^{5/2}}{5 a} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^(3/2)*x^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.67117, size = 17, normalized size = 0.74 \[ \frac{2 x^{\frac{5}{2}} \left (a + \frac{b}{x}\right )^{\frac{5}{2}}}{5 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**(3/2)*x**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0373606, size = 30, normalized size = 1.3 \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b)^2}{5 a} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^(3/2)*x^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 25, normalized size = 1.1 \[{\frac{2\,ax+2\,b}{5\,a} \left ({\frac{ax+b}{x}} \right ) ^{{\frac{3}{2}}}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^(3/2)*x^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44039, size = 23, normalized size = 1. \[ \frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{5}{2}} x^{\frac{5}{2}}}{5 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^(3/2)*x^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.241455, size = 47, normalized size = 2.04 \[ \frac{2 \,{\left (a^{2} x^{2} + 2 \, a b x + b^{2}\right )} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{5 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^(3/2)*x^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**(3/2)*x**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.226788, size = 16, normalized size = 0.7 \[ \frac{2 \,{\left (a x + b\right )}^{\frac{5}{2}}}{5 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^(3/2)*x^(3/2),x, algorithm="giac")
[Out]