Optimal. Leaf size=37 \[ a^3 \log (x)-\frac{3 a^2 b}{x}-\frac{3 a b^2}{2 x^2}-\frac{b^3}{3 x^3} \]
[Out]
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Rubi [A] time = 0.0425869, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ a^3 \log (x)-\frac{3 a^2 b}{x}-\frac{3 a b^2}{2 x^2}-\frac{b^3}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3/x,x]
[Out]
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Rubi in Sympy [A] time = 7.992, size = 34, normalized size = 0.92 \[ a^{3} \log{\left (x \right )} - \frac{3 a^{2} b}{x} - \frac{3 a b^{2}}{2 x^{2}} - \frac{b^{3}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3/x,x)
[Out]
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Mathematica [A] time = 0.0061008, size = 37, normalized size = 1. \[ a^3 \log (x)-\frac{3 a^2 b}{x}-\frac{3 a b^2}{2 x^2}-\frac{b^3}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3/x,x]
[Out]
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Maple [A] time = 0.01, size = 34, normalized size = 0.9 \[ -{\frac{{b}^{3}}{3\,{x}^{3}}}-{\frac{3\,a{b}^{2}}{2\,{x}^{2}}}-3\,{\frac{{a}^{2}b}{x}}+{a}^{3}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3/x,x)
[Out]
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Maxima [A] time = 1.43989, size = 46, normalized size = 1.24 \[ a^{3} \log \left (x\right ) - \frac{18 \, a^{2} b x^{2} + 9 \, a b^{2} x + 2 \, b^{3}}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217569, size = 50, normalized size = 1.35 \[ \frac{6 \, a^{3} x^{3} \log \left (x\right ) - 18 \, a^{2} b x^{2} - 9 \, a b^{2} x - 2 \, b^{3}}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.35708, size = 34, normalized size = 0.92 \[ a^{3} \log{\left (x \right )} - \frac{18 a^{2} b x^{2} + 9 a b^{2} x + 2 b^{3}}{6 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3/x,x)
[Out]
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GIAC/XCAS [A] time = 0.225378, size = 47, normalized size = 1.27 \[ a^{3}{\rm ln}\left ({\left | x \right |}\right ) - \frac{18 \, a^{2} b x^{2} + 9 \, a b^{2} x + 2 \, b^{3}}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x,x, algorithm="giac")
[Out]