Optimal. Leaf size=24 \[ -3 x+x \log (x)+(x+1) \log (x+1)+(x+2) \log (x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {2295, 2389} \[ -3 x+x \log (x)+(x+1) \log (x+1)+(x+2) \log (x+2) \]
Antiderivative was successfully verified.
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Rule 2295
Rule 2389
Rubi steps
\begin {align*} \int (\log (x)+\log (1+x)+\log (2+x)) \, dx &=\int \log (x) \, dx+\int \log (1+x) \, dx+\int \log (2+x) \, dx\\ &=-x+x \log (x)+\operatorname {Subst}(\int \log (x) \, dx,x,1+x)+\operatorname {Subst}(\int \log (x) \, dx,x,2+x)\\ &=-3 x+x \log (x)+(1+x) \log (1+x)+(2+x) \log (2+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.25 \[ -3 x+x \log (x)+x \log (x+1)+x \log (x+2)+\log (x+1)+2 \log (x+2) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 24, normalized size = 1.00 \[ {\left (x + 2\right )} \log \left (x + 2\right ) + {\left (x + 1\right )} \log \left (x + 1\right ) + x \log \relax (x) - 3 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 25, normalized size = 1.04 \[ {\left (x + 2\right )} \log \left (x + 2\right ) + {\left (x + 1\right )} \log \left (x + 1\right ) + x \log \relax (x) - 3 \, x - 3 \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 26, normalized size = 1.08 \[ x \ln \relax (x )-3 x +\left (x +1\right ) \ln \left (x +1\right )+\left (x +2\right ) \ln \left (x +2\right )-3 \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 25, normalized size = 1.04 \[ {\left (x + 2\right )} \log \left (x + 2\right ) + {\left (x + 1\right )} \log \left (x + 1\right ) + x \log \relax (x) - 3 \, x - 3 \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.44, size = 51, normalized size = 2.12 \[ \ln \left (x+1\right )-3\,x+2\,\ln \left (x+2\right )+x\,\ln \left (x+1\right )+x\,\ln \relax (x)+\frac {\ln \left (x+2\right )\,\left (x^3+3\,x^2+2\,x\right )}{\left (x+1\right )\,\left (x+2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.20, size = 37, normalized size = 1.54 \[ x \log {\relax (x )} - 3 x + \left (x + \frac {1}{2}\right ) \log {\left (x + 1 \right )} + \left (x + 1\right ) \log {\left (x + 2 \right )} + \frac {\log {\left (x + 1 \right )}}{2} + \log {\left (x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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