Optimal. Leaf size=19 \[ -\frac{a}{2 x^2}-\frac{3 b}{5 x^{5/3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0155531, antiderivative size = 19, 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 \[ -\frac{a}{2 x^2}-\frac{3 b}{5 x^{5/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))/x^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.94582, size = 17, normalized size = 0.89 \[ - \frac{a}{2 x^{2}} - \frac{3 b}{5 x^{\frac{5}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00757016, size = 19, normalized size = 1. \[ -\frac{a}{2 x^2}-\frac{3 b}{5 x^{5/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))/x^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 14, normalized size = 0.7 \[ -{\frac{a}{2\,{x}^{2}}}-{\frac{3\,b}{5}{x}^{-{\frac{5}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))/x^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43992, size = 20, normalized size = 1.05 \[ -\frac{6 \, b x^{\frac{1}{3}} + 5 \, a}{10 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)/x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215202, size = 20, normalized size = 1.05 \[ -\frac{6 \, b x^{\frac{1}{3}} + 5 \, a}{10 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)/x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.79186, size = 17, normalized size = 0.89 \[ - \frac{a}{2 x^{2}} - \frac{3 b}{5 x^{\frac{5}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.237336, size = 20, normalized size = 1.05 \[ -\frac{6 \, b x^{\frac{1}{3}} + 5 \, a}{10 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)/x^3,x, algorithm="giac")
[Out]