Optimal. Leaf size=17 \[ -\frac{a}{x}-\frac{3 b}{2 x^{2/3}} \]
[Out]
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Rubi [A] time = 0.0164993, antiderivative size = 17, 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 \[ -\frac{a}{x}-\frac{3 b}{2 x^{2/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))/x^2,x]
[Out]
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Rubi in Sympy [A] time = 3.0318, size = 14, normalized size = 0.82 \[ - \frac{a}{x} - \frac{3 b}{2 x^{\frac{2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))/x**2,x)
[Out]
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Mathematica [A] time = 0.00750872, size = 17, normalized size = 1. \[ -\frac{a}{x}-\frac{3 b}{2 x^{2/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))/x^2,x]
[Out]
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Maple [A] time = 0.008, size = 14, normalized size = 0.8 \[ -{\frac{a}{x}}-{\frac{3\,b}{2}{x}^{-{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))/x^2,x)
[Out]
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Maxima [A] time = 1.44402, size = 20, normalized size = 1.18 \[ -\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212827, size = 20, normalized size = 1.18 \[ -\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.51015, size = 14, normalized size = 0.82 \[ - \frac{a}{x} - \frac{3 b}{2 x^{\frac{2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.246131, size = 20, normalized size = 1.18 \[ -\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)/x^2,x, algorithm="giac")
[Out]