Optimal. Leaf size=76 \[ \frac{1364}{16807 (1-2 x)}-\frac{829}{16807 (3 x+2)}+\frac{121}{2401 (1-2 x)^2}+\frac{32}{2401 (3 x+2)^2}-\frac{1}{1029 (3 x+2)^3}-\frac{5750 \log (1-2 x)}{117649}+\frac{5750 \log (3 x+2)}{117649} \]
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Rubi [A] time = 0.0382317, antiderivative size = 76, 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} \[ \frac{1364}{16807 (1-2 x)}-\frac{829}{16807 (3 x+2)}+\frac{121}{2401 (1-2 x)^2}+\frac{32}{2401 (3 x+2)^2}-\frac{1}{1029 (3 x+2)^3}-\frac{5750 \log (1-2 x)}{117649}+\frac{5750 \log (3 x+2)}{117649} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)^4} \, dx &=\int \left (-\frac{484}{2401 (-1+2 x)^3}+\frac{2728}{16807 (-1+2 x)^2}-\frac{11500}{117649 (-1+2 x)}+\frac{3}{343 (2+3 x)^4}-\frac{192}{2401 (2+3 x)^3}+\frac{2487}{16807 (2+3 x)^2}+\frac{17250}{117649 (2+3 x)}\right ) \, dx\\ &=\frac{121}{2401 (1-2 x)^2}+\frac{1364}{16807 (1-2 x)}-\frac{1}{1029 (2+3 x)^3}+\frac{32}{2401 (2+3 x)^2}-\frac{829}{16807 (2+3 x)}-\frac{5750 \log (1-2 x)}{117649}+\frac{5750 \log (2+3 x)}{117649}\\ \end{align*}
Mathematica [A] time = 0.0468887, size = 57, normalized size = 0.75 \[ \frac{\frac{7 \left (-310500 x^4-284625 x^3+117875 x^2+180100 x+44411\right )}{(1-2 x)^2 (3 x+2)^3}-17250 \log (1-2 x)+17250 \log (6 x+4)}{352947} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 63, normalized size = 0.8 \begin{align*}{\frac{121}{2401\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{1364}{33614\,x-16807}}-{\frac{5750\,\ln \left ( 2\,x-1 \right ) }{117649}}-{\frac{1}{1029\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{32}{2401\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{829}{33614+50421\,x}}+{\frac{5750\,\ln \left ( 2+3\,x \right ) }{117649}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02617, size = 89, normalized size = 1.17 \begin{align*} -\frac{310500 \, x^{4} + 284625 \, x^{3} - 117875 \, x^{2} - 180100 \, x - 44411}{50421 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} + \frac{5750}{117649} \, \log \left (3 \, x + 2\right ) - \frac{5750}{117649} \, \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 = 1.5064, size = 350, normalized size = 4.61 \begin{align*} -\frac{2173500 \, x^{4} + 1992375 \, x^{3} - 825125 \, x^{2} - 17250 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 17250 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (2 \, x - 1\right ) - 1260700 \, x - 310877}{352947 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.185196, size = 65, normalized size = 0.86 \begin{align*} - \frac{310500 x^{4} + 284625 x^{3} - 117875 x^{2} - 180100 x - 44411}{5445468 x^{5} + 5445468 x^{4} - 2268945 x^{3} - 2924418 x^{2} + 201684 x + 403368} - \frac{5750 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{5750 \log{\left (x + \frac{2}{3} \right )}}{117649} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.35532, size = 74, normalized size = 0.97 \begin{align*} -\frac{310500 \, x^{4} + 284625 \, x^{3} - 117875 \, x^{2} - 180100 \, x - 44411}{50421 \,{\left (3 \, x + 2\right )}^{3}{\left (2 \, x - 1\right )}^{2}} + \frac{5750}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{5750}{117649} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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