Optimal. Leaf size=65 \[ \frac {128}{2401 (1-2 x)}-\frac {87}{2401 (3 x+2)}+\frac {11}{343 (1-2 x)^2}+\frac {3}{686 (3 x+2)^2}-\frac {558 \log (1-2 x)}{16807}+\frac {558 \log (3 x+2)}{16807} \]
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Rubi [A] time = 0.03, antiderivative size = 65, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} \frac {128}{2401 (1-2 x)}-\frac {87}{2401 (3 x+2)}+\frac {11}{343 (1-2 x)^2}+\frac {3}{686 (3 x+2)^2}-\frac {558 \log (1-2 x)}{16807}+\frac {558 \log (3 x+2)}{16807} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^3 (2+3 x)^3} \, dx &=\int \left (-\frac {44}{343 (-1+2 x)^3}+\frac {256}{2401 (-1+2 x)^2}-\frac {1116}{16807 (-1+2 x)}-\frac {9}{343 (2+3 x)^3}+\frac {261}{2401 (2+3 x)^2}+\frac {1674}{16807 (2+3 x)}\right ) \, dx\\ &=\frac {11}{343 (1-2 x)^2}+\frac {128}{2401 (1-2 x)}+\frac {3}{686 (2+3 x)^2}-\frac {87}{2401 (2+3 x)}-\frac {558 \log (1-2 x)}{16807}+\frac {558 \log (2+3 x)}{16807}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 48, normalized size = 0.74 \begin {gather*} \frac {\frac {7 \left (-6696 x^3-1674 x^2+3658 x+1313\right )}{\left (6 x^2+x-2\right )^2}-1116 \log (1-2 x)+1116 \log (3 x+2)}{33614} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3+5 x}{(1-2 x)^3 (2+3 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.82, size = 95, normalized size = 1.46 \begin {gather*} -\frac {46872 \, x^{3} + 11718 \, x^{2} - 1116 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 1116 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (2 \, x - 1\right ) - 25606 \, x - 9191}{33614 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 46, normalized size = 0.71 \begin {gather*} -\frac {6696 \, x^{3} + 1674 \, x^{2} - 3658 \, x - 1313}{4802 \, {\left (6 \, x^{2} + x - 2\right )}^{2}} + \frac {558}{16807} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {558}{16807} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 54, normalized size = 0.83 \begin {gather*} -\frac {558 \ln \left (2 x -1\right )}{16807}+\frac {558 \ln \left (3 x +2\right )}{16807}+\frac {3}{686 \left (3 x +2\right )^{2}}-\frac {87}{2401 \left (3 x +2\right )}+\frac {11}{343 \left (2 x -1\right )^{2}}-\frac {128}{2401 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 56, normalized size = 0.86 \begin {gather*} -\frac {6696 \, x^{3} + 1674 \, x^{2} - 3658 \, x - 1313}{4802 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} + \frac {558}{16807} \, \log \left (3 \, x + 2\right ) - \frac {558}{16807} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 45, normalized size = 0.69 \begin {gather*} \frac {1116\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{16807}+\frac {-\frac {93\,x^3}{2401}-\frac {93\,x^2}{9604}+\frac {1829\,x}{86436}+\frac {1313}{172872}}{x^4+\frac {x^3}{3}-\frac {23\,x^2}{36}-\frac {x}{9}+\frac {1}{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 54, normalized size = 0.83 \begin {gather*} - \frac {6696 x^{3} + 1674 x^{2} - 3658 x - 1313}{172872 x^{4} + 57624 x^{3} - 110446 x^{2} - 19208 x + 19208} - \frac {558 \log {\left (x - \frac {1}{2} \right )}}{16807} + \frac {558 \log {\left (x + \frac {2}{3} \right )}}{16807} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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