Optimal. Leaf size=23 \[ \frac{\log (x)}{3}-\log (x+1)+\frac{2}{3} \log (2 x+3) \]
[Out]
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Rubi [A] time = 0.0272626, antiderivative size = 23, 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 \[ \frac{\log (x)}{3}-\log (x+1)+\frac{2}{3} \log (2 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/(x*(1 + x)*(3 + 2*x)),x]
[Out]
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Rubi in Sympy [A] time = 1.89823, size = 19, normalized size = 0.83 \[ \frac{\log{\left (x \right )}}{3} - \log{\left (x + 1 \right )} + \frac{2 \log{\left (2 x + 3 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(1+x)/(3+2*x),x)
[Out]
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Mathematica [A] time = 0.00727353, size = 23, normalized size = 1. \[ \frac{\log (x)}{3}-\log (x+1)+\frac{2}{3} \log (2 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(1 + x)*(3 + 2*x)),x]
[Out]
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Maple [A] time = 0.01, size = 20, normalized size = 0.9 \[{\frac{\ln \left ( x \right ) }{3}}-\ln \left ( 1+x \right ) +{\frac{2\,\ln \left ( 3+2\,x \right ) }{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(1+x)/(3+2*x),x)
[Out]
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Maxima [A] time = 1.33825, size = 26, normalized size = 1.13 \[ \frac{2}{3} \, \log \left (2 \, x + 3\right ) - \log \left (x + 1\right ) + \frac{1}{3} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x + 3)*(x + 1)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210755, size = 26, normalized size = 1.13 \[ \frac{2}{3} \, \log \left (2 \, x + 3\right ) - \log \left (x + 1\right ) + \frac{1}{3} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x + 3)*(x + 1)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.14694, size = 19, normalized size = 0.83 \[ \frac{\log{\left (x \right )}}{3} - \log{\left (x + 1 \right )} + \frac{2 \log{\left (x + \frac{3}{2} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(1+x)/(3+2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.21507, size = 30, normalized size = 1.3 \[ \frac{2}{3} \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) -{\rm ln}\left ({\left | x + 1 \right |}\right ) + \frac{1}{3} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x + 3)*(x + 1)*x),x, algorithm="giac")
[Out]