Optimal. Leaf size=21 \[ \frac{2}{5} a x^{5/2}+\frac{2}{3} b x^{3/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0138204, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{2}{5} a x^{5/2}+\frac{2}{3} b x^{3/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)*x^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.78427, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 b x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)*x**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00625823, size = 17, normalized size = 0.81 \[ \frac{2}{15} x^{3/2} (3 a x+5 b) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)*x^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 14, normalized size = 0.7 \[{\frac{6\,ax+10\,b}{15}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)*x^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43811, size = 20, normalized size = 0.95 \[ \frac{2}{15} \,{\left (3 \, a + \frac{5 \, b}{x}\right )} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)*x^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.227104, size = 22, normalized size = 1.05 \[ \frac{2}{15} \,{\left (3 \, a x^{2} + 5 \, b x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)*x^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.83358, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 b x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)*x**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.229559, size = 18, normalized size = 0.86 \[ \frac{2}{5} \, a x^{\frac{5}{2}} + \frac{2}{3} \, b x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)*x^(3/2),x, algorithm="giac")
[Out]