Optimal. Leaf size=40 \[ -\frac{a^3}{2 x^2}+3 a^2 b \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4} \]
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Rubi [A] time = 0.0589127, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ -\frac{a^3}{2 x^2}+3 a^2 b \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[(a/x + b*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{3}}{2 x^{2}} + \frac{3 a^{2} b \log{\left (x^{2} \right )}}{2} + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} \int ^{x^{2}} x\, dx}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a/x+b*x)**3,x)
[Out]
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Mathematica [A] time = 0.0109767, size = 40, normalized size = 1. \[ -\frac{a^3}{2 x^2}+3 a^2 b \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[(a/x + b*x)^3,x]
[Out]
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Maple [A] time = 0.009, size = 35, normalized size = 0.9 \[ -{\frac{{a}^{3}}{2\,{x}^{2}}}+{\frac{3\,a{b}^{2}{x}^{2}}{2}}+{\frac{{b}^{3}{x}^{4}}{4}}+3\,{a}^{2}b\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a/x+b*x)^3,x)
[Out]
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Maxima [A] time = 1.39367, size = 46, normalized size = 1.15 \[ \frac{1}{4} \, b^{3} x^{4} + \frac{3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b \log \left (x\right ) - \frac{a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a/x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220705, size = 51, normalized size = 1.27 \[ \frac{b^{3} x^{6} + 6 \, a b^{2} x^{4} + 12 \, a^{2} b x^{2} \log \left (x\right ) - 2 \, a^{3}}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a/x)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.17231, size = 37, normalized size = 0.92 \[ - \frac{a^{3}}{2 x^{2}} + 3 a^{2} b \log{\left (x \right )} + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a/x+b*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.220201, size = 62, normalized size = 1.55 \[ \frac{1}{4} \, b^{3} x^{4} + \frac{3}{2} \, a b^{2} x^{2} + \frac{3}{2} \, a^{2} b{\rm ln}\left (x^{2}\right ) - \frac{3 \, a^{2} b x^{2} + a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a/x)^3,x, algorithm="giac")
[Out]