Optimal. Leaf size=19 \[ -\frac{a}{3 x^3}-\frac{3 b}{8 x^{8/3}} \]
[Out]
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Rubi [A] time = 0.0162039, 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 \[ -\frac{a}{3 x^3}-\frac{3 b}{8 x^{8/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))/x^4,x]
[Out]
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Rubi in Sympy [A] time = 2.89295, size = 17, normalized size = 0.89 \[ - \frac{a}{3 x^{3}} - \frac{3 b}{8 x^{\frac{8}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))/x**4,x)
[Out]
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Mathematica [A] time = 0.00626751, size = 19, normalized size = 1. \[ -\frac{a}{3 x^3}-\frac{3 b}{8 x^{8/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))/x^4,x]
[Out]
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Maple [A] time = 0.008, size = 14, normalized size = 0.7 \[ -{\frac{a}{3\,{x}^{3}}}-{\frac{3\,b}{8}{x}^{-{\frac{8}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))/x^4,x)
[Out]
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Maxima [A] time = 1.4458, size = 20, normalized size = 1.05 \[ -\frac{9 \, b x^{\frac{1}{3}} + 8 \, a}{24 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213195, size = 20, normalized size = 1.05 \[ -\frac{9 \, b x^{\frac{1}{3}} + 8 \, a}{24 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.00004, size = 17, normalized size = 0.89 \[ - \frac{a}{3 x^{3}} - \frac{3 b}{8 x^{\frac{8}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.248079, size = 20, normalized size = 1.05 \[ -\frac{9 \, b x^{\frac{1}{3}} + 8 \, a}{24 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)/x^4,x, algorithm="giac")
[Out]