Optimal. Leaf size=65 \[ -\frac{1331}{2401 (3 x+2)}+\frac{3469}{18522 (3 x+2)^2}-\frac{103}{3969 (3 x+2)^3}+\frac{1}{756 (3 x+2)^4}-\frac{2662 \log (1-2 x)}{16807}+\frac{2662 \log (3 x+2)}{16807} \]
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Rubi [A] time = 0.0266106, 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} \[ -\frac{1331}{2401 (3 x+2)}+\frac{3469}{18522 (3 x+2)^2}-\frac{103}{3969 (3 x+2)^3}+\frac{1}{756 (3 x+2)^4}-\frac{2662 \log (1-2 x)}{16807}+\frac{2662 \log (3 x+2)}{16807} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^5} \, dx &=\int \left (-\frac{5324}{16807 (-1+2 x)}-\frac{1}{63 (2+3 x)^5}+\frac{103}{441 (2+3 x)^4}-\frac{3469}{3087 (2+3 x)^3}+\frac{3993}{2401 (2+3 x)^2}+\frac{7986}{16807 (2+3 x)}\right ) \, dx\\ &=\frac{1}{756 (2+3 x)^4}-\frac{103}{3969 (2+3 x)^3}+\frac{3469}{18522 (2+3 x)^2}-\frac{1331}{2401 (2+3 x)}-\frac{2662 \log (1-2 x)}{16807}+\frac{2662 \log (2+3 x)}{16807}\\ \end{align*}
Mathematica [A] time = 0.0317636, size = 47, normalized size = 0.72 \[ \frac{2 \left (-\frac{7 \left (11643588 x^3+21975894 x^2+13836972 x+2906507\right )}{8 (3 x+2)^4}-107811 \log (1-2 x)+107811 \log (6 x+4)\right )}{1361367} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 54, normalized size = 0.8 \begin{align*} -{\frac{2662\,\ln \left ( 2\,x-1 \right ) }{16807}}+{\frac{1}{756\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{103}{3969\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{3469}{18522\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{1331}{4802+7203\,x}}+{\frac{2662\,\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 = 1.23511, size = 76, normalized size = 1.17 \begin{align*} -\frac{11643588 \, x^{3} + 21975894 \, x^{2} + 13836972 \, x + 2906507}{777924 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{2662}{16807} \, \log \left (3 \, x + 2\right ) - \frac{2662}{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 = 1.25343, size = 316, normalized size = 4.86 \begin{align*} -\frac{81505116 \, x^{3} + 153831258 \, x^{2} - 862488 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 862488 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (2 \, x - 1\right ) + 96858804 \, x + 20345549}{5445468 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.175441, size = 54, normalized size = 0.83 \begin{align*} - \frac{11643588 x^{3} + 21975894 x^{2} + 13836972 x + 2906507}{63011844 x^{4} + 168031584 x^{3} + 168031584 x^{2} + 74680704 x + 12446784} - \frac{2662 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{2662 \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 = 1.66253, size = 70, normalized size = 1.08 \begin{align*} -\frac{1331}{2401 \,{\left (3 \, x + 2\right )}} + \frac{3469}{18522 \,{\left (3 \, x + 2\right )}^{2}} - \frac{103}{3969 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1}{756 \,{\left (3 \, x + 2\right )}^{4}} - \frac{2662}{16807} \, \log \left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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