Optimal. Leaf size=23 \[ -\frac {1}{2} \log (1+x)+2 \log (2+x)-\frac {3}{2} \log (3+x) \]
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Rubi [A]
time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {153}
\begin {gather*} -\frac {1}{2} \log (x+1)+2 \log (x+2)-\frac {3}{2} \log (x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 153
Rubi steps
\begin {align*} \int \frac {x}{(1+x) (2+x) (3+x)} \, dx &=\int \left (-\frac {1}{2 (1+x)}+\frac {2}{2+x}-\frac {3}{2 (3+x)}\right ) \, dx\\ &=-\frac {1}{2} \log (1+x)+2 \log (2+x)-\frac {3}{2} \log (3+x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 23, normalized size = 1.00 \begin {gather*} -\frac {1}{2} \log (1+x)+2 \log (2+x)-\frac {3}{2} \log (3+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 20, normalized size = 0.87
method | result | size |
default | \(-\frac {\ln \left (1+x \right )}{2}+2 \ln \left (2+x \right )-\frac {3 \ln \left (3+x \right )}{2}\) | \(20\) |
norman | \(-\frac {\ln \left (1+x \right )}{2}+2 \ln \left (2+x \right )-\frac {3 \ln \left (3+x \right )}{2}\) | \(20\) |
risch | \(-\frac {\ln \left (1+x \right )}{2}+2 \ln \left (2+x \right )-\frac {3 \ln \left (3+x \right )}{2}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 3.61, size = 19, normalized size = 0.83 \begin {gather*} -\frac {3}{2} \, \log \left (x + 3\right ) + 2 \, \log \left (x + 2\right ) - \frac {1}{2} \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.30, size = 19, normalized size = 0.83 \begin {gather*} -\frac {3}{2} \, \log \left (x + 3\right ) + 2 \, \log \left (x + 2\right ) - \frac {1}{2} \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 20, normalized size = 0.87 \begin {gather*} - \frac {\log {\left (x + 1 \right )}}{2} + 2 \log {\left (x + 2 \right )} - \frac {3 \log {\left (x + 3 \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.45, size = 22, normalized size = 0.96 \begin {gather*} -\frac {3}{2} \, \log \left ({\left | x + 3 \right |}\right ) + 2 \, \log \left ({\left | x + 2 \right |}\right ) - \frac {1}{2} \, \log \left ({\left | x + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 19, normalized size = 0.83 \begin {gather*} 2\,\ln \left (x+2\right )-\frac {\ln \left (x+1\right )}{2}-\frac {3\,\ln \left (x+3\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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