Optimal. Leaf size=34 \[ -\frac{a^2}{3 x^3}-\frac{3 a b}{5 x^{10/3}}-\frac{3 b^2}{11 x^{11/3}} \]
[Out]
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Rubi [A] time = 0.0501065, antiderivative size = 34, 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 \[ -\frac{a^2}{3 x^3}-\frac{3 a b}{5 x^{10/3}}-\frac{3 b^2}{11 x^{11/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))^2/x^4,x]
[Out]
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Rubi in Sympy [A] time = 8.28133, size = 32, normalized size = 0.94 \[ - \frac{a^{2}}{3 x^{3}} - \frac{3 a b}{5 x^{\frac{10}{3}}} - \frac{3 b^{2}}{11 x^{\frac{11}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))**2/x**4,x)
[Out]
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Mathematica [A] time = 0.0180864, size = 34, normalized size = 1. \[ -\frac{a^2}{3 x^3}-\frac{3 a b}{5 x^{10/3}}-\frac{3 b^2}{11 x^{11/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))^2/x^4,x]
[Out]
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Maple [A] time = 0.008, size = 25, normalized size = 0.7 \[ -{\frac{3\,{b}^{2}}{11}{x}^{-{\frac{11}{3}}}}-{\frac{3\,ab}{5}{x}^{-{\frac{10}{3}}}}-{\frac{{a}^{2}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))^2/x^4,x)
[Out]
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Maxima [A] time = 1.44088, size = 201, normalized size = 5.91 \[ -\frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{11}}{11 \, b^{9}} + \frac{12 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{10} a}{5 \, b^{9}} - \frac{28 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{9} a^{2}}{3 \, b^{9}} + \frac{21 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{8} a^{3}}{b^{9}} - \frac{30 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{7} a^{4}}{b^{9}} + \frac{28 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{6} a^{5}}{b^{9}} - \frac{84 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{5} a^{6}}{5 \, b^{9}} + \frac{6 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{4} a^{7}}{b^{9}} - \frac{{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{3} a^{8}}{b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22193, size = 35, normalized size = 1.03 \[ -\frac{55 \, a^{2} x^{\frac{2}{3}} + 99 \, a b x^{\frac{1}{3}} + 45 \, b^{2}}{165 \, x^{\frac{11}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 11.4025, size = 32, normalized size = 0.94 \[ - \frac{a^{2}}{3 x^{3}} - \frac{3 a b}{5 x^{\frac{10}{3}}} - \frac{3 b^{2}}{11 x^{\frac{11}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))**2/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.210804, size = 35, normalized size = 1.03 \[ -\frac{55 \, a^{2} x^{\frac{2}{3}} + 99 \, a b x^{\frac{1}{3}} + 45 \, b^{2}}{165 \, x^{\frac{11}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2/x^4,x, algorithm="giac")
[Out]