Optimal. Leaf size=76 \[ \frac{484}{16807 (1-2 x)}-\frac{1364}{16807 (3 x+2)}-\frac{319}{4802 (3 x+2)^2}+\frac{22}{1029 (3 x+2)^3}-\frac{1}{588 (3 x+2)^4}-\frac{4180 \log (1-2 x)}{117649}+\frac{4180 \log (3 x+2)}{117649} \]
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Rubi [A] time = 0.0363819, 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} \[ \frac{484}{16807 (1-2 x)}-\frac{1364}{16807 (3 x+2)}-\frac{319}{4802 (3 x+2)^2}+\frac{22}{1029 (3 x+2)^3}-\frac{1}{588 (3 x+2)^4}-\frac{4180 \log (1-2 x)}{117649}+\frac{4180 \log (3 x+2)}{117649} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^5} \, dx &=\int \left (\frac{968}{16807 (-1+2 x)^2}-\frac{8360}{117649 (-1+2 x)}+\frac{1}{49 (2+3 x)^5}-\frac{66}{343 (2+3 x)^4}+\frac{957}{2401 (2+3 x)^3}+\frac{4092}{16807 (2+3 x)^2}+\frac{12540}{117649 (2+3 x)}\right ) \, dx\\ &=\frac{484}{16807 (1-2 x)}-\frac{1}{588 (2+3 x)^4}+\frac{22}{1029 (2+3 x)^3}-\frac{319}{4802 (2+3 x)^2}-\frac{1364}{16807 (2+3 x)}-\frac{4180 \log (1-2 x)}{117649}+\frac{4180 \log (2+3 x)}{117649}\\ \end{align*}
Mathematica [A] time = 0.0383373, size = 59, normalized size = 0.78 \[ \frac{2 \left (-\frac{7 \left (1354320 x^4+2821500 x^3+1724250 x^2+172990 x-83327\right )}{8 (2 x-1) (3 x+2)^4}-6270 \log (1-2 x)+6270 \log (6 x+4)\right )}{352947} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 63, normalized size = 0.8 \begin{align*} -{\frac{484}{33614\,x-16807}}-{\frac{4180\,\ln \left ( 2\,x-1 \right ) }{117649}}-{\frac{1}{588\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{22}{1029\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{319}{4802\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{1364}{33614+50421\,x}}+{\frac{4180\,\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 = 1.02492, size = 89, normalized size = 1.17 \begin{align*} -\frac{1354320 \, x^{4} + 2821500 \, x^{3} + 1724250 \, x^{2} + 172990 \, x - 83327}{201684 \,{\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} + \frac{4180}{117649} \, \log \left (3 \, x + 2\right ) - \frac{4180}{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 = 1.32727, size = 367, normalized size = 4.83 \begin{align*} -\frac{9480240 \, x^{4} + 19750500 \, x^{3} + 12069750 \, x^{2} - 50160 \,{\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (3 \, x + 2\right ) + 50160 \,{\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (2 \, x - 1\right ) + 1210930 \, x - 583289}{1411788 \,{\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.176498, size = 65, normalized size = 0.86 \begin{align*} - \frac{1354320 x^{4} + 2821500 x^{3} + 1724250 x^{2} + 172990 x - 83327}{32672808 x^{5} + 70791084 x^{4} + 43563744 x^{3} - 4840416 x^{2} - 12907776 x - 3226944} - \frac{4180 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{4180 \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 = 2.24501, size = 90, normalized size = 1.18 \begin{align*} -\frac{1364}{16807 \,{\left (3 \, x + 2\right )}} + \frac{2904}{117649 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}} - \frac{319}{4802 \,{\left (3 \, x + 2\right )}^{2}} + \frac{22}{1029 \,{\left (3 \, x + 2\right )}^{3}} - \frac{1}{588 \,{\left (3 \, x + 2\right )}^{4}} - \frac{4180}{117649} \, \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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