Optimal. Leaf size=65 \[ \frac{1331}{2401 (1-2 x)}+\frac{363}{2401 (3 x+2)}-\frac{101}{6174 (3 x+2)^2}+\frac{1}{1323 (3 x+2)^3}-\frac{3267 \log (1-2 x)}{16807}+\frac{3267 \log (3 x+2)}{16807} \]
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Rubi [A] time = 0.02997, 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} \[ \frac{1331}{2401 (1-2 x)}+\frac{363}{2401 (3 x+2)}-\frac{101}{6174 (3 x+2)^2}+\frac{1}{1323 (3 x+2)^3}-\frac{3267 \log (1-2 x)}{16807}+\frac{3267 \log (3 x+2)}{16807} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx &=\int \left (\frac{2662}{2401 (-1+2 x)^2}-\frac{6534}{16807 (-1+2 x)}-\frac{1}{147 (2+3 x)^4}+\frac{101}{1029 (2+3 x)^3}-\frac{1089}{2401 (2+3 x)^2}+\frac{9801}{16807 (2+3 x)}\right ) \, dx\\ &=\frac{1331}{2401 (1-2 x)}+\frac{1}{1323 (2+3 x)^3}-\frac{101}{6174 (2+3 x)^2}+\frac{363}{2401 (2+3 x)}-\frac{3267 \log (1-2 x)}{16807}+\frac{3267 \log (2+3 x)}{16807}\\ \end{align*}
Mathematica [A] time = 0.0392992, size = 62, normalized size = 0.95 \[ \frac{\frac{7}{2} \left (\frac{19602}{3 x+2}-\frac{2121}{(3 x+2)^2}+\frac{98}{(3 x+2)^3}+\frac{71874}{1-2 x}\right )-88209 \log (1-2 x)+88209 \log (6 x+4)}{453789} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 54, normalized size = 0.8 \begin{align*} -{\frac{1331}{4802\,x-2401}}-{\frac{3267\,\ln \left ( 2\,x-1 \right ) }{16807}}+{\frac{1}{1323\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{101}{6174\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{363}{4802+7203\,x}}+{\frac{3267\,\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 = 1.0838, size = 76, normalized size = 1.17 \begin{align*} -\frac{1587762 \, x^{3} + 3599892 \, x^{2} + 2667797 \, x + 649256}{129654 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac{3267}{16807} \, \log \left (3 \, x + 2\right ) - \frac{3267}{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 = 1.27916, size = 300, normalized size = 4.62 \begin{align*} -\frac{11114334 \, x^{3} + 25199244 \, x^{2} - 176418 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 176418 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 18674579 \, x + 4544792}{907578 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.166226, size = 54, normalized size = 0.83 \begin{align*} - \frac{1587762 x^{3} + 3599892 x^{2} + 2667797 x + 649256}{7001316 x^{4} + 10501974 x^{3} + 2333772 x^{2} - 2593080 x - 1037232} - \frac{3267 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{3267 \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 = 1.62826, size = 81, normalized size = 1.25 \begin{align*} -\frac{1331}{2401 \,{\left (2 \, x - 1\right )}} - \frac{2 \,{\left (\frac{43645}{2 \, x - 1} + \frac{50127}{{\left (2 \, x - 1\right )}^{2}} + 9502\right )}}{16807 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{3}} + \frac{3267}{16807} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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