Optimal. Leaf size=65 \[ -\frac{363}{2401 (1-2 x)}-\frac{33}{2401 (3 x+2)}+\frac{1331}{1372 (1-2 x)^2}+\frac{1}{2058 (3 x+2)^2}+\frac{1023 \log (1-2 x)}{16807}-\frac{1023 \log (3 x+2)}{16807} \]
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Rubi [A] time = 0.028958, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{363}{2401 (1-2 x)}-\frac{33}{2401 (3 x+2)}+\frac{1331}{1372 (1-2 x)^2}+\frac{1}{2058 (3 x+2)^2}+\frac{1023 \log (1-2 x)}{16807}-\frac{1023 \log (3 x+2)}{16807} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^3} \, dx &=\int \left (-\frac{1331}{343 (-1+2 x)^3}-\frac{726}{2401 (-1+2 x)^2}+\frac{2046}{16807 (-1+2 x)}-\frac{1}{343 (2+3 x)^3}+\frac{99}{2401 (2+3 x)^2}-\frac{3069}{16807 (2+3 x)}\right ) \, dx\\ &=\frac{1331}{1372 (1-2 x)^2}-\frac{363}{2401 (1-2 x)}+\frac{1}{2058 (2+3 x)^2}-\frac{33}{2401 (2+3 x)}+\frac{1023 \log (1-2 x)}{16807}-\frac{1023 \log (2+3 x)}{16807}\\ \end{align*}
Mathematica [A] time = 0.0315647, size = 48, normalized size = 0.74 \[ \frac{\frac{7 \left (73656 x^3+318539 x^2+319912 x+93602\right )}{\left (6 x^2+x-2\right )^2}+12276 \log (1-2 x)-12276 \log (3 x+2)}{201684} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 54, normalized size = 0.8 \begin{align*}{\frac{1331}{1372\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{363}{4802\,x-2401}}+{\frac{1023\,\ln \left ( 2\,x-1 \right ) }{16807}}+{\frac{1}{2058\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{33}{4802+7203\,x}}-{\frac{1023\,\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 = 1.06087, size = 76, normalized size = 1.17 \begin{align*} \frac{73656 \, x^{3} + 318539 \, x^{2} + 319912 \, x + 93602}{28812 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} - \frac{1023}{16807} \, \log \left (3 \, x + 2\right ) + \frac{1023}{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 = 1.52674, size = 285, normalized size = 4.38 \begin{align*} \frac{515592 \, x^{3} + 2229773 \, x^{2} - 12276 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 12276 \,{\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (2 \, x - 1\right ) + 2239384 \, x + 655214}{201684 \,{\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 = 0.175456, size = 54, normalized size = 0.83 \begin{align*} \frac{73656 x^{3} + 318539 x^{2} + 319912 x + 93602}{1037232 x^{4} + 345744 x^{3} - 662676 x^{2} - 115248 x + 115248} + \frac{1023 \log{\left (x - \frac{1}{2} \right )}}{16807} - \frac{1023 \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 = 3.7145, size = 62, normalized size = 0.95 \begin{align*} \frac{73656 \, x^{3} + 318539 \, x^{2} + 319912 \, x + 93602}{28812 \,{\left (6 \, x^{2} + x - 2\right )}^{2}} - \frac{1023}{16807} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac{1023}{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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