Optimal. Leaf size=46 \[ \frac {1}{x+2}+\frac {5}{4 (x+3)}+\frac {1}{4 (x+3)^2}+\frac {1}{8} \log (x+1)+2 \log (x+2)-\frac {17}{8} \log (x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {88} \[ \frac {1}{x+2}+\frac {5}{4 (x+3)}+\frac {1}{4 (x+3)^2}+\frac {1}{8} \log (x+1)+2 \log (x+2)-\frac {17}{8} \log (x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1+x) (2+x)^2 (3+x)^3} \, dx &=\int \left (\frac {1}{8 (1+x)}-\frac {1}{(2+x)^2}+\frac {2}{2+x}-\frac {1}{2 (3+x)^3}-\frac {5}{4 (3+x)^2}-\frac {17}{8 (3+x)}\right ) \, dx\\ &=\frac {1}{2+x}+\frac {1}{4 (3+x)^2}+\frac {5}{4 (3+x)}+\frac {1}{8} \log (1+x)+2 \log (2+x)-\frac {17}{8} \log (3+x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 44, normalized size = 0.96 \[ \frac {1}{8} \left (\frac {8}{x+2}+\frac {10}{x+3}+\frac {2}{(x+3)^2}+\log (-x-1)+16 \log (x+2)-17 \log (x+3)\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.63, size = 83, normalized size = 1.80 \[ \frac {18 \, x^{2} - 17 \, {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )} \log \left (x + 3\right ) + 16 \, {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )} \log \left (x + 2\right ) + {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )} \log \left (x + 1\right ) + 100 \, x + 136}{8 \, {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 52, normalized size = 1.13 \[ \frac {1}{x + 2} - \frac {\frac {7}{x + 2} + 6}{4 \, {\left (\frac {1}{x + 2} + 1\right )}^{2}} + \frac {1}{8} \, \log \left ({\left | -\frac {1}{x + 2} + 1 \right |}\right ) - \frac {17}{8} \, \log \left ({\left | -\frac {1}{x + 2} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 39, normalized size = 0.85 \[ \frac {\ln \left (x +1\right )}{8}+2 \ln \left (x +2\right )-\frac {17 \ln \left (x +3\right )}{8}+\frac {1}{x +2}+\frac {1}{4 \left (x +3\right )^{2}}+\frac {5}{4 \left (x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 46, normalized size = 1.00 \[ \frac {9 \, x^{2} + 50 \, x + 68}{4 \, {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )}} - \frac {17}{8} \, \log \left (x + 3\right ) + 2 \, \log \left (x + 2\right ) + \frac {1}{8} \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 45, normalized size = 0.98 \[ \frac {\ln \left (x+1\right )}{8}+2\,\ln \left (x+2\right )-\frac {17\,\ln \left (x+3\right )}{8}+\frac {\frac {9\,x^2}{4}+\frac {25\,x}{2}+17}{x^3+8\,x^2+21\,x+18} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 46, normalized size = 1.00 \[ \frac {9 x^{2} + 50 x + 68}{4 x^{3} + 32 x^{2} + 84 x + 72} + \frac {\log {\left (x + 1 \right )}}{8} + 2 \log {\left (x + 2 \right )} - \frac {17 \log {\left (x + 3 \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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