Optimal. Leaf size=34 \[ -\frac{a^2}{2 x^2}-\frac{6 a b}{5 x^{5/3}}-\frac{3 b^2}{4 x^{4/3}} \]
[Out]
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Rubi [A] time = 0.0433039, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{a^2}{2 x^2}-\frac{6 a b}{5 x^{5/3}}-\frac{3 b^2}{4 x^{4/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^2/x^3,x]
[Out]
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Rubi in Sympy [A] time = 6.76713, size = 32, normalized size = 0.94 \[ - \frac{a^{2}}{2 x^{2}} - \frac{6 a b}{5 x^{\frac{5}{3}}} - \frac{3 b^{2}}{4 x^{\frac{4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**2/x**3,x)
[Out]
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Mathematica [A] time = 0.0128438, size = 34, normalized size = 1. \[ -\frac{a^2}{2 x^2}-\frac{6 a b}{5 x^{5/3}}-\frac{3 b^2}{4 x^{4/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^2/x^3,x]
[Out]
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Maple [A] time = 0.008, size = 25, normalized size = 0.7 \[ -{\frac{{a}^{2}}{2\,{x}^{2}}}-{\frac{6\,ab}{5}{x}^{-{\frac{5}{3}}}}-{\frac{3\,{b}^{2}}{4}{x}^{-{\frac{4}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^2/x^3,x)
[Out]
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Maxima [A] time = 1.42443, size = 35, normalized size = 1.03 \[ -\frac{15 \, b^{2} x^{\frac{2}{3}} + 24 \, a b x^{\frac{1}{3}} + 10 \, a^{2}}{20 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212666, size = 35, normalized size = 1.03 \[ -\frac{15 \, b^{2} x^{\frac{2}{3}} + 24 \, a b x^{\frac{1}{3}} + 10 \, a^{2}}{20 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.99564, size = 32, normalized size = 0.94 \[ - \frac{a^{2}}{2 x^{2}} - \frac{6 a b}{5 x^{\frac{5}{3}}} - \frac{3 b^{2}}{4 x^{\frac{4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**2/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.25413, size = 35, normalized size = 1.03 \[ -\frac{15 \, b^{2} x^{\frac{2}{3}} + 24 \, a b x^{\frac{1}{3}} + 10 \, a^{2}}{20 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2/x^3,x, algorithm="giac")
[Out]