Optimal. Leaf size=47 \[ -\frac{a^3}{3 x^3}-\frac{9 a^2 b}{10 x^{10/3}}-\frac{9 a b^2}{11 x^{11/3}}-\frac{b^3}{4 x^4} \]
[Out]
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Rubi [A] time = 0.0631515, antiderivative size = 47, 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 \[ -\frac{a^3}{3 x^3}-\frac{9 a^2 b}{10 x^{10/3}}-\frac{9 a b^2}{11 x^{11/3}}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))^3/x^4,x]
[Out]
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Rubi in Sympy [A] time = 10.5861, size = 44, normalized size = 0.94 \[ - \frac{a^{3}}{3 x^{3}} - \frac{9 a^{2} b}{10 x^{\frac{10}{3}}} - \frac{9 a b^{2}}{11 x^{\frac{11}{3}}} - \frac{b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))**3/x**4,x)
[Out]
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Mathematica [A] time = 0.0159019, size = 41, normalized size = 0.87 \[ -\frac{220 a^3 x+594 a^2 b x^{2/3}+540 a b^2 \sqrt [3]{x}+165 b^3}{660 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))^3/x^4,x]
[Out]
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Maple [A] time = 0.009, size = 36, normalized size = 0.8 \[ -{\frac{{b}^{3}}{4\,{x}^{4}}}-{\frac{9\,a{b}^{2}}{11}{x}^{-{\frac{11}{3}}}}-{\frac{9\,{a}^{2}b}{10}{x}^{-{\frac{10}{3}}}}-{\frac{{a}^{3}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))^3/x^4,x)
[Out]
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Maxima [A] time = 1.44016, size = 201, normalized size = 4.28 \[ -\frac{{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{12}}{4 \, b^{9}} + \frac{24 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{11} a}{11 \, b^{9}} - \frac{42 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{10} a^{2}}{5 \, b^{9}} + \frac{56 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{9} a^{3}}{3 \, b^{9}} - \frac{105 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{8} a^{4}}{4 \, b^{9}} + \frac{24 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{7} a^{5}}{b^{9}} - \frac{14 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{6} a^{6}}{b^{9}} + \frac{24 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{5} a^{7}}{5 \, b^{9}} - \frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{4} a^{8}}{4 \, b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223081, size = 47, normalized size = 1. \[ -\frac{220 \, a^{3} x + 594 \, a^{2} b x^{\frac{2}{3}} + 540 \, a b^{2} x^{\frac{1}{3}} + 165 \, b^{3}}{660 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 14.1571, size = 44, normalized size = 0.94 \[ - \frac{a^{3}}{3 x^{3}} - \frac{9 a^{2} b}{10 x^{\frac{10}{3}}} - \frac{9 a b^{2}}{11 x^{\frac{11}{3}}} - \frac{b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))**3/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.212173, size = 47, normalized size = 1. \[ -\frac{220 \, a^{3} x + 594 \, a^{2} b x^{\frac{2}{3}} + 540 \, a b^{2} x^{\frac{1}{3}} + 165 \, b^{3}}{660 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3/x^4,x, algorithm="giac")
[Out]