Optimal. Leaf size=22 \[ \frac{a^2 x^2}{2}+2 a b x+b^2 \log (x) \]
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Rubi [A] time = 0.0268559, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{a^2 x^2}{2}+2 a b x+b^2 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2*x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{2} \int x\, dx + 2 a b x + b^{2} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**2*x,x)
[Out]
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Mathematica [A] time = 0.00190614, size = 22, normalized size = 1. \[ \frac{a^2 x^2}{2}+2 a b x+b^2 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2*x,x]
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Maple [A] time = 0.003, size = 21, normalized size = 1. \[ 2\,abx+{\frac{{a}^{2}{x}^{2}}{2}}+{b}^{2}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^2*x,x)
[Out]
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Maxima [A] time = 1.43738, size = 27, normalized size = 1.23 \[ \frac{1}{2} \, a^{2} x^{2} + 2 \, a b x + b^{2} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223945, size = 27, normalized size = 1.23 \[ \frac{1}{2} \, a^{2} x^{2} + 2 \, a b x + b^{2} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.03465, size = 20, normalized size = 0.91 \[ \frac{a^{2} x^{2}}{2} + 2 a b x + b^{2} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**2*x,x)
[Out]
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GIAC/XCAS [A] time = 0.221837, size = 28, normalized size = 1.27 \[ \frac{1}{2} \, a^{2} x^{2} + 2 \, a b x + b^{2}{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x,x, algorithm="giac")
[Out]