Optimal. Leaf size=32 \[ -\frac{a^2}{x}-\frac{3 a b}{2 x^{4/3}}-\frac{3 b^2}{5 x^{5/3}} \]
[Out]
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Rubi [A] time = 0.0480176, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\frac{a^2}{x}-\frac{3 a b}{2 x^{4/3}}-\frac{3 b^2}{5 x^{5/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))^2/x^2,x]
[Out]
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Rubi in Sympy [A] time = 8.01112, size = 29, normalized size = 0.91 \[ - \frac{a^{2}}{x} - \frac{3 a b}{2 x^{\frac{4}{3}}} - \frac{3 b^{2}}{5 x^{\frac{5}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))**2/x**2,x)
[Out]
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Mathematica [A] time = 0.0201804, size = 32, normalized size = 1. \[ -\frac{a^2}{x}-\frac{3 a b}{2 x^{4/3}}-\frac{3 b^2}{5 x^{5/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))^2/x^2,x]
[Out]
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Maple [A] time = 0.009, size = 25, normalized size = 0.8 \[ -{\frac{3\,{b}^{2}}{5}{x}^{-{\frac{5}{3}}}}-{\frac{3\,ab}{2}{x}^{-{\frac{4}{3}}}}-{\frac{{a}^{2}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))^2/x^2,x)
[Out]
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Maxima [A] time = 1.43103, size = 63, normalized size = 1.97 \[ -\frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{5}}{5 \, b^{3}} + \frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{4} a}{2 \, b^{3}} - \frac{{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{3} a^{2}}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220105, size = 35, normalized size = 1.09 \[ -\frac{10 \, a^{2} x^{\frac{2}{3}} + 15 \, a b x^{\frac{1}{3}} + 6 \, b^{2}}{10 \, x^{\frac{5}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.11919, size = 29, normalized size = 0.91 \[ - \frac{a^{2}}{x} - \frac{3 a b}{2 x^{\frac{4}{3}}} - \frac{3 b^{2}}{5 x^{\frac{5}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))**2/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211076, size = 35, normalized size = 1.09 \[ -\frac{10 \, a^{2} x^{\frac{2}{3}} + 15 \, a b x^{\frac{1}{3}} + 6 \, b^{2}}{10 \, x^{\frac{5}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2/x^2,x, algorithm="giac")
[Out]