Optimal. Leaf size=45 \[ -\frac{a^3}{x}-\frac{9 a^2 b}{4 x^{4/3}}-\frac{9 a b^2}{5 x^{5/3}}-\frac{b^3}{2 x^2} \]
[Out]
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Rubi [A] time = 0.0618226, antiderivative size = 45, 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 \[ -\frac{a^3}{x}-\frac{9 a^2 b}{4 x^{4/3}}-\frac{9 a b^2}{5 x^{5/3}}-\frac{b^3}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))^3/x^2,x]
[Out]
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Rubi in Sympy [A] time = 10.2589, size = 41, normalized size = 0.91 \[ - \frac{a^{3}}{x} - \frac{9 a^{2} b}{4 x^{\frac{4}{3}}} - \frac{9 a b^{2}}{5 x^{\frac{5}{3}}} - \frac{b^{3}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))**3/x**2,x)
[Out]
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Mathematica [A] time = 0.018159, size = 41, normalized size = 0.91 \[ -\frac{20 a^3 x+45 a^2 b x^{2/3}+36 a b^2 \sqrt [3]{x}+10 b^3}{20 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))^3/x^2,x]
[Out]
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Maple [A] time = 0.008, size = 36, normalized size = 0.8 \[ -{\frac{{b}^{3}}{2\,{x}^{2}}}-{\frac{9\,a{b}^{2}}{5}{x}^{-{\frac{5}{3}}}}-{\frac{9\,{a}^{2}b}{4}{x}^{-{\frac{4}{3}}}}-{\frac{{a}^{3}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))^3/x^2,x)
[Out]
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Maxima [A] time = 1.43777, size = 63, normalized size = 1.4 \[ -\frac{{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{6}}{2 \, b^{3}} + \frac{6 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{5} a}{5 \, b^{3}} - \frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{4} a^{2}}{4 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225213, size = 47, normalized size = 1.04 \[ -\frac{20 \, a^{3} x + 45 \, a^{2} b x^{\frac{2}{3}} + 36 \, a b^{2} x^{\frac{1}{3}} + 10 \, b^{3}}{20 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.21301, size = 41, normalized size = 0.91 \[ - \frac{a^{3}}{x} - \frac{9 a^{2} b}{4 x^{\frac{4}{3}}} - \frac{9 a b^{2}}{5 x^{\frac{5}{3}}} - \frac{b^{3}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))**3/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.212779, size = 47, normalized size = 1.04 \[ -\frac{20 \, a^{3} x + 45 \, a^{2} b x^{\frac{2}{3}} + 36 \, a b^{2} x^{\frac{1}{3}} + 10 \, b^{3}}{20 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3/x^2,x, algorithm="giac")
[Out]