Optimal. Leaf size=55 \[ -\frac{216 x^5}{125}+\frac{189 x^4}{125}+\frac{786 x^3}{625}-\frac{12077 x^2}{6250}+\frac{1998 x}{3125}-\frac{1331}{78125 (5 x+3)}+\frac{11253 \log (5 x+3)}{78125} \]
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Rubi [A] time = 0.0267051, antiderivative size = 55, 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} \[ -\frac{216 x^5}{125}+\frac{189 x^4}{125}+\frac{786 x^3}{625}-\frac{12077 x^2}{6250}+\frac{1998 x}{3125}-\frac{1331}{78125 (5 x+3)}+\frac{11253 \log (5 x+3)}{78125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)^3}{(3+5 x)^2} \, dx &=\int \left (\frac{1998}{3125}-\frac{12077 x}{3125}+\frac{2358 x^2}{625}+\frac{756 x^3}{125}-\frac{216 x^4}{25}+\frac{1331}{15625 (3+5 x)^2}+\frac{11253}{15625 (3+5 x)}\right ) \, dx\\ &=\frac{1998 x}{3125}-\frac{12077 x^2}{6250}+\frac{786 x^3}{625}+\frac{189 x^4}{125}-\frac{216 x^5}{125}-\frac{1331}{78125 (3+5 x)}+\frac{11253 \log (3+5 x)}{78125}\\ \end{align*}
Mathematica [A] time = 0.0155753, size = 54, normalized size = 0.98 \[ \frac{-6750000 x^6+1856250 x^5+8456250 x^4-4600625 x^3-2031375 x^2+5485095 x+112530 (5 x+3) \log (5 x+3)+2378647}{781250 (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 42, normalized size = 0.8 \begin{align*}{\frac{1998\,x}{3125}}-{\frac{12077\,{x}^{2}}{6250}}+{\frac{786\,{x}^{3}}{625}}+{\frac{189\,{x}^{4}}{125}}-{\frac{216\,{x}^{5}}{125}}-{\frac{1331}{234375+390625\,x}}+{\frac{11253\,\ln \left ( 3+5\,x \right ) }{78125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.41195, size = 55, normalized size = 1. \begin{align*} -\frac{216}{125} \, x^{5} + \frac{189}{125} \, x^{4} + \frac{786}{625} \, x^{3} - \frac{12077}{6250} \, x^{2} + \frac{1998}{3125} \, x - \frac{1331}{78125 \,{\left (5 \, x + 3\right )}} + \frac{11253}{78125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.26284, size = 185, normalized size = 3.36 \begin{align*} -\frac{1350000 \, x^{6} - 371250 \, x^{5} - 1691250 \, x^{4} + 920125 \, x^{3} + 406275 \, x^{2} - 22506 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 299700 \, x + 2662}{156250 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.10523, size = 48, normalized size = 0.87 \begin{align*} - \frac{216 x^{5}}{125} + \frac{189 x^{4}}{125} + \frac{786 x^{3}}{625} - \frac{12077 x^{2}}{6250} + \frac{1998 x}{3125} + \frac{11253 \log{\left (5 x + 3 \right )}}{78125} - \frac{1331}{390625 x + 234375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.76644, size = 101, normalized size = 1.84 \begin{align*} \frac{1}{781250} \,{\left (5 \, x + 3\right )}^{5}{\left (\frac{8370}{5 \, x + 3} - \frac{53700}{{\left (5 \, x + 3\right )}^{2}} + \frac{87575}{{\left (5 \, x + 3\right )}^{3}} + \frac{295350}{{\left (5 \, x + 3\right )}^{4}} - 432\right )} - \frac{1331}{78125 \,{\left (5 \, x + 3\right )}} - \frac{11253}{78125} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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