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 = 0.034599, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{128}{2401 (1-2 x)}-\frac{87}{2401 (3 x+2)}+\frac{11}{343 (1-2 x)^2}+\frac{3}{686 (3 x+2)^2}-\frac{558 \log (1-2 x)}{16807}+\frac{558 \log (3 x+2)}{16807} \]
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*}
Mathematica [A] time = 0.0248281, size = 48, normalized size = 0.74 \[ \frac{\frac{7 \left (-6696 x^3-1674 x^2+3658 x+1313\right )}{\left (6 x^2+x-2\right )^2}-1116 \log (1-2 x)+1116 \log (3 x+2)}{33614} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 54, normalized size = 0.8 \begin{align*}{\frac{11}{343\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{128}{4802\,x-2401}}-{\frac{558\,\ln \left ( 2\,x-1 \right ) }{16807}}+{\frac{3}{686\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{87}{4802+7203\,x}}+{\frac{558\,\ln \left ( 2+3\,x \right ) }{16807}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10602, size = 76, normalized size = 1.17 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29314, size = 273, normalized size = 4.2 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.161573, size = 54, normalized size = 0.83 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.31312, size = 62, normalized size = 0.95 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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