Optimal. Leaf size=34 \[ \frac{3}{2 (1-x)}-\frac{5}{4} \log (1-x)+2 \log (x)-\frac{3}{4} \log (x+1) \]
[Out]
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Rubi [A] time = 0.0894976, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{3}{2 (1-x)}-\frac{5}{4} \log (1-x)+2 \log (x)-\frac{3}{4} \log (x+1) \]
Antiderivative was successfully verified.
[In] Int[(2 + x^2)/((-1 + x)^2*x*(1 + x)),x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+2)/(-1+x)**2/x/(1+x),x)
[Out]
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Mathematica [A] time = 0.0253209, size = 32, normalized size = 0.94 \[ -\frac{3}{2 (x-1)}-\frac{5}{4} \log (1-x)+2 \log (x)-\frac{3}{4} \log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[(2 + x^2)/((-1 + x)^2*x*(1 + x)),x]
[Out]
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Maple [A] time = 0.013, size = 25, normalized size = 0.7 \[ -{\frac{3}{2\,x-2}}-{\frac{5\,\ln \left ( -1+x \right ) }{4}}-{\frac{3\,\ln \left ( 1+x \right ) }{4}}+2\,\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+2)/(-1+x)^2/x/(1+x),x)
[Out]
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Maxima [A] time = 0.804361, size = 32, normalized size = 0.94 \[ -\frac{3}{2 \,{\left (x - 1\right )}} - \frac{3}{4} \, \log \left (x + 1\right ) - \frac{5}{4} \, \log \left (x - 1\right ) + 2 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2)/((x + 1)*(x - 1)^2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253541, size = 46, normalized size = 1.35 \[ -\frac{3 \,{\left (x - 1\right )} \log \left (x + 1\right ) + 5 \,{\left (x - 1\right )} \log \left (x - 1\right ) - 8 \,{\left (x - 1\right )} \log \left (x\right ) + 6}{4 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2)/((x + 1)*(x - 1)^2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.336332, size = 27, normalized size = 0.79 \[ 2 \log{\left (x \right )} - \frac{5 \log{\left (x - 1 \right )}}{4} - \frac{3 \log{\left (x + 1 \right )}}{4} - \frac{3}{2 x - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+2)/(-1+x)**2/x/(1+x),x)
[Out]
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GIAC/XCAS [A] time = 0.261878, size = 46, normalized size = 1.35 \[ -\frac{3}{2 \,{\left (x - 1\right )}} + 2 \,{\rm ln}\left ({\left | -\frac{1}{x - 1} - 1 \right |}\right ) - \frac{3}{4} \,{\rm ln}\left ({\left | -\frac{2}{x - 1} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2)/((x + 1)*(x - 1)^2*x),x, algorithm="giac")
[Out]