Optimal. Leaf size=28 \[ \frac{4}{5 (x+2)}+\frac{9}{25} \log (3-x)+\frac{16}{25} \log (x+2) \]
[Out]
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Rubi [A] time = 0.0325676, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{4}{5 (x+2)}+\frac{9}{25} \log (3-x)+\frac{16}{25} \log (x+2) \]
Antiderivative was successfully verified.
[In] Int[x^2/((-3 + x)*(2 + x)^2),x]
[Out]
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Rubi in Sympy [A] time = 2.05015, size = 22, normalized size = 0.79 \[ \frac{9 \log{\left (- x + 3 \right )}}{25} + \frac{16 \log{\left (x + 2 \right )}}{25} + \frac{4}{5 \left (x + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(-3+x)/(2+x)**2,x)
[Out]
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Mathematica [A] time = 0.0235232, size = 26, normalized size = 0.93 \[ \frac{4}{5 (x+2)}+\frac{9}{25} \log (x-3)+\frac{16}{25} \log (x+2) \]
Antiderivative was successfully verified.
[In] Integrate[x^2/((-3 + x)*(2 + x)^2),x]
[Out]
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Maple [A] time = 0.01, size = 21, normalized size = 0.8 \[{\frac{9\,\ln \left ( -3+x \right ) }{25}}+{\frac{4}{10+5\,x}}+{\frac{16\,\ln \left ( 2+x \right ) }{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(-3+x)/(2+x)^2,x)
[Out]
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Maxima [A] time = 1.36354, size = 27, normalized size = 0.96 \[ \frac{4}{5 \,{\left (x + 2\right )}} + \frac{16}{25} \, \log \left (x + 2\right ) + \frac{9}{25} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((x + 2)^2*(x - 3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203826, size = 36, normalized size = 1.29 \[ \frac{16 \,{\left (x + 2\right )} \log \left (x + 2\right ) + 9 \,{\left (x + 2\right )} \log \left (x - 3\right ) + 20}{25 \,{\left (x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((x + 2)^2*(x - 3)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.129302, size = 22, normalized size = 0.79 \[ \frac{9 \log{\left (x - 3 \right )}}{25} + \frac{16 \log{\left (x + 2 \right )}}{25} + \frac{4}{5 x + 10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(-3+x)/(2+x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.206013, size = 35, normalized size = 1.25 \[ \frac{4}{5 \,{\left (x + 2\right )}} +{\rm ln}\left ({\left | x + 2 \right |}\right ) + \frac{9}{25} \,{\rm ln}\left ({\left | -\frac{5}{x + 2} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((x + 2)^2*(x - 3)),x, algorithm="giac")
[Out]