Optimal. Leaf size=17 \[ 5 \log (2-x)-6 \log (x)+\log (x+2) \]
[Out]
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Rubi [A] time = 0.041434, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ 5 \log (2-x)-6 \log (x)+\log (x+2) \]
Antiderivative was successfully verified.
[In] Int[(24 + 8*x)/(x*(-4 + x^2)),x]
[Out]
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Rubi in Sympy [A] time = 5.6143, size = 15, normalized size = 0.88 \[ - 6 \log{\left (x \right )} + 5 \log{\left (- x + 2 \right )} + \log{\left (x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((24+8*x)/x/(x**2-4),x)
[Out]
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Mathematica [A] time = 0.00966221, size = 27, normalized size = 1.59 \[ 8 \left (\frac{5}{8} \log (2-x)-\frac{3 \log (x)}{4}+\frac{1}{8} \log (x+2)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(24 + 8*x)/(x*(-4 + x^2)),x]
[Out]
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Maple [A] time = 0.01, size = 16, normalized size = 0.9 \[ \ln \left ( 2+x \right ) -6\,\ln \left ( x \right ) +5\,\ln \left ( x-2 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((24+8*x)/x/(x^2-4),x)
[Out]
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Maxima [A] time = 0.796886, size = 20, normalized size = 1.18 \[ \log \left (x + 2\right ) + 5 \, \log \left (x - 2\right ) - 6 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(8*(x + 3)/((x^2 - 4)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.27961, size = 20, normalized size = 1.18 \[ \log \left (x + 2\right ) + 5 \, \log \left (x - 2\right ) - 6 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(8*(x + 3)/((x^2 - 4)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.264976, size = 15, normalized size = 0.88 \[ - 6 \log{\left (x \right )} + 5 \log{\left (x - 2 \right )} + \log{\left (x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((24+8*x)/x/(x**2-4),x)
[Out]
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GIAC/XCAS [A] time = 0.259095, size = 24, normalized size = 1.41 \[{\rm ln}\left ({\left | x + 2 \right |}\right ) + 5 \,{\rm ln}\left ({\left | x - 2 \right |}\right ) - 6 \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(8*(x + 3)/((x^2 - 4)*x),x, algorithm="giac")
[Out]