Optimal. Leaf size=13 \[ \frac{a x^2}{2}+b \log (x) \]
[Out]
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Rubi [A] time = 0.0135458, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{a x^2}{2}+b \log (x) \]
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. \[ a \int x\, dx + b \log{\left (x \right )} \]
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 = 0.00526564, size = 13, normalized size = 1. \[ \frac{a x^2}{2}+b \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)*x,x]
[Out]
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Maple [A] time = 0.003, size = 12, normalized size = 0.9 \[{\frac{a{x}^{2}}{2}}+b\ln \left ( x \right ) \]
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 = 1.42977, size = 19, normalized size = 1.46 \[ \frac{1}{2} \, a x^{2} + \frac{1}{2} \, b \log \left (x^{2}\right ) \]
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 = 0.234629, size = 15, normalized size = 1.15 \[ \frac{1}{2} \, a x^{2} + b \log \left (x\right ) \]
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 = 0.143045, size = 10, normalized size = 0.77 \[ \frac{a x^{2}}{2} + b \log{\left (x \right )} \]
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 = 0.228145, size = 16, normalized size = 1.23 \[ \frac{1}{2} \, a x^{2} + b{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)*x,x, algorithm="giac")
[Out]