Optimal. Leaf size=23 \[ -\frac{1}{2} \log (x+1)+2 \log (x+2)-\frac{3}{2} \log (x+3) \]
[Out]
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Rubi [A] time = 0.0438025, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{1}{2} \log (x+1)+2 \log (x+2)-\frac{3}{2} \log (x+3) \]
Antiderivative was successfully verified.
[In] Int[x/((1 + x)*(2 + x)*(3 + x)),x]
[Out]
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Rubi in Sympy [A] time = 5.41681, size = 20, normalized size = 0.87 \[ - \frac{\log{\left (x + 1 \right )}}{2} + 2 \log{\left (x + 2 \right )} - \frac{3 \log{\left (x + 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(1+x)/(2+x)/(3+x),x)
[Out]
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Mathematica [A] time = 0.0114391, size = 23, normalized size = 1. \[ -\frac{1}{2} \log (x+1)+2 \log (x+2)-\frac{3}{2} \log (x+3) \]
Antiderivative was successfully verified.
[In] Integrate[x/((1 + x)*(2 + x)*(3 + x)),x]
[Out]
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Maple [A] time = 0.01, size = 20, normalized size = 0.9 \[ -{\frac{\ln \left ( 1+x \right ) }{2}}+2\,\ln \left ( 2+x \right ) -{\frac{3\,\ln \left ( 3+x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(1+x)/(2+x)/(3+x),x)
[Out]
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Maxima [A] time = 1.35939, size = 26, normalized size = 1.13 \[ -\frac{3}{2} \, \log \left (x + 3\right ) + 2 \, \log \left (x + 2\right ) - \frac{1}{2} \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x + 3)*(x + 2)*(x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.259598, size = 26, normalized size = 1.13 \[ -\frac{3}{2} \, \log \left (x + 3\right ) + 2 \, \log \left (x + 2\right ) - \frac{1}{2} \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x + 3)*(x + 2)*(x + 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.285438, size = 20, normalized size = 0.87 \[ - \frac{\log{\left (x + 1 \right )}}{2} + 2 \log{\left (x + 2 \right )} - \frac{3 \log{\left (x + 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(1+x)/(2+x)/(3+x),x)
[Out]
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GIAC/XCAS [A] time = 0.214715, size = 30, normalized size = 1.3 \[ -\frac{3}{2} \,{\rm ln}\left ({\left | x + 3 \right |}\right ) + 2 \,{\rm ln}\left ({\left | x + 2 \right |}\right ) - \frac{1}{2} \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x + 3)*(x + 2)*(x + 1)),x, algorithm="giac")
[Out]