Optimal. Leaf size=39 \[ a^3 \log (x)-\frac{9 a^2 b}{\sqrt [3]{x}}-\frac{9 a b^2}{2 x^{2/3}}-\frac{b^3}{x} \]
[Out]
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Rubi [A] time = 0.0601997, antiderivative size = 39, 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 \[ a^3 \log (x)-\frac{9 a^2 b}{\sqrt [3]{x}}-\frac{9 a b^2}{2 x^{2/3}}-\frac{b^3}{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))^3/x,x]
[Out]
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Rubi in Sympy [A] time = 9.86226, size = 41, normalized size = 1.05 \[ 3 a^{3} \log{\left (\sqrt [3]{x} \right )} - \frac{9 a^{2} b}{\sqrt [3]{x}} - \frac{9 a b^{2}}{2 x^{\frac{2}{3}}} - \frac{b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))**3/x,x)
[Out]
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Mathematica [A] time = 0.0358506, size = 40, normalized size = 1.03 \[ a^3 \log (x)-\frac{b \left (18 a^2 x^{2/3}+9 a b \sqrt [3]{x}+2 b^2\right )}{2 x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))^3/x,x]
[Out]
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Maple [A] time = 0.01, size = 34, normalized size = 0.9 \[ -{\frac{{b}^{3}}{x}}-{\frac{9\,a{b}^{2}}{2}{x}^{-{\frac{2}{3}}}}-9\,{\frac{{a}^{2}b}{\sqrt [3]{x}}}+{a}^{3}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))^3/x,x)
[Out]
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Maxima [A] time = 1.42827, size = 45, normalized size = 1.15 \[ a^{3} \log \left (x\right ) - \frac{9 \, a^{2} b}{x^{\frac{1}{3}}} - \frac{9 \, a b^{2}}{2 \, x^{\frac{2}{3}}} - \frac{b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22596, size = 53, normalized size = 1.36 \[ \frac{6 \, a^{3} x \log \left (x^{\frac{1}{3}}\right ) - 18 \, a^{2} b x^{\frac{2}{3}} - 9 \, a b^{2} x^{\frac{1}{3}} - 2 \, b^{3}}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.31978, size = 36, normalized size = 0.92 \[ a^{3} \log{\left (x \right )} - \frac{9 a^{2} b}{\sqrt [3]{x}} - \frac{9 a b^{2}}{2 x^{\frac{2}{3}}} - \frac{b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))**3/x,x)
[Out]
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GIAC/XCAS [A] time = 0.214629, size = 50, normalized size = 1.28 \[ a^{3}{\rm ln}\left ({\left | x \right |}\right ) - \frac{18 \, a^{2} b x^{\frac{2}{3}} + 9 \, a b^{2} x^{\frac{1}{3}} + 2 \, b^{3}}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3/x,x, algorithm="giac")
[Out]