Optimal. Leaf size=14 \[ \frac{1}{x}+2 \log (x)+3 \log (x+2) \]
[Out]
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Rubi [A] time = 0.0420218, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{1}{x}+2 \log (x)+3 \log (x+2) \]
Antiderivative was successfully verified.
[In] Int[(-2 + 3*x + 5*x^2)/(2*x^2 + x^3),x]
[Out]
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Rubi in Sympy [A] time = 3.16199, size = 14, normalized size = 1. \[ 2 \log{\left (x \right )} + 3 \log{\left (x + 2 \right )} + \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5*x**2+3*x-2)/(x**3+2*x**2),x)
[Out]
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Mathematica [A] time = 0.00573666, size = 14, normalized size = 1. \[ \frac{1}{x}+2 \log (x)+3 \log (x+2) \]
Antiderivative was successfully verified.
[In] Integrate[(-2 + 3*x + 5*x^2)/(2*x^2 + x^3),x]
[Out]
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Maple [A] time = 0.01, size = 15, normalized size = 1.1 \[{x}^{-1}+2\,\ln \left ( x \right ) +3\,\ln \left ( 2+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5*x^2+3*x-2)/(x^3+2*x^2),x)
[Out]
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Maxima [A] time = 1.37504, size = 19, normalized size = 1.36 \[ \frac{1}{x} + 3 \, \log \left (x + 2\right ) + 2 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x^2 + 3*x - 2)/(x^3 + 2*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205905, size = 24, normalized size = 1.71 \[ \frac{3 \, x \log \left (x + 2\right ) + 2 \, x \log \left (x\right ) + 1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x^2 + 3*x - 2)/(x^3 + 2*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.115328, size = 14, normalized size = 1. \[ 2 \log{\left (x \right )} + 3 \log{\left (x + 2 \right )} + \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x**2+3*x-2)/(x**3+2*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.211322, size = 22, normalized size = 1.57 \[ \frac{1}{x} + 3 \,{\rm ln}\left ({\left | x + 2 \right |}\right ) + 2 \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x^2 + 3*x - 2)/(x^3 + 2*x^2),x, algorithm="giac")
[Out]