Optimal. Leaf size=45 \[ -\frac{a^3}{2 x^2}-\frac{9 a^2 b}{5 x^{5/3}}-\frac{9 a b^2}{4 x^{4/3}}-\frac{b^3}{x} \]
[Out]
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Rubi [A] time = 0.0554227, antiderivative size = 45, 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 \[ -\frac{a^3}{2 x^2}-\frac{9 a^2 b}{5 x^{5/3}}-\frac{9 a b^2}{4 x^{4/3}}-\frac{b^3}{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^3/x^3,x]
[Out]
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Rubi in Sympy [A] time = 8.97845, size = 41, normalized size = 0.91 \[ - \frac{a^{3}}{2 x^{2}} - \frac{9 a^{2} b}{5 x^{\frac{5}{3}}} - \frac{9 a b^{2}}{4 x^{\frac{4}{3}}} - \frac{b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**3/x**3,x)
[Out]
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Mathematica [A] time = 0.0159044, size = 41, normalized size = 0.91 \[ -\frac{10 a^3+36 a^2 b \sqrt [3]{x}+45 a b^2 x^{2/3}+20 b^3 x}{20 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^3/x^3,x]
[Out]
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Maple [A] time = 0.008, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{2\,{x}^{2}}}-{\frac{9\,{a}^{2}b}{5}{x}^{-{\frac{5}{3}}}}-{\frac{9\,a{b}^{2}}{4}{x}^{-{\frac{4}{3}}}}-{\frac{{b}^{3}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^3/x^3,x)
[Out]
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Maxima [A] time = 1.44767, size = 47, normalized size = 1.04 \[ -\frac{20 \, b^{3} x + 45 \, a b^{2} x^{\frac{2}{3}} + 36 \, a^{2} b x^{\frac{1}{3}} + 10 \, a^{3}}{20 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213877, size = 47, normalized size = 1.04 \[ -\frac{20 \, b^{3} x + 45 \, a b^{2} x^{\frac{2}{3}} + 36 \, a^{2} b x^{\frac{1}{3}} + 10 \, a^{3}}{20 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.10645, size = 41, normalized size = 0.91 \[ - \frac{a^{3}}{2 x^{2}} - \frac{9 a^{2} b}{5 x^{\frac{5}{3}}} - \frac{9 a b^{2}}{4 x^{\frac{4}{3}}} - \frac{b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**3/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.220307, size = 47, normalized size = 1.04 \[ -\frac{20 \, b^{3} x + 45 \, a b^{2} x^{\frac{2}{3}} + 36 \, a^{2} b x^{\frac{1}{3}} + 10 \, a^{3}}{20 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3/x^3,x, algorithm="giac")
[Out]