Optimal. Leaf size=48 \[ -\frac{18 x^4}{25}+\frac{164 x^3}{125}-\frac{427 x^2}{625}-\frac{1179 x}{3125}-\frac{1331}{15625 (5 x+3)}+\frac{1452 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0223557, antiderivative size = 48, 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} \[ -\frac{18 x^4}{25}+\frac{164 x^3}{125}-\frac{427 x^2}{625}-\frac{1179 x}{3125}-\frac{1331}{15625 (5 x+3)}+\frac{1452 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)^2}{(3+5 x)^2} \, dx &=\int \left (-\frac{1179}{3125}-\frac{854 x}{625}+\frac{492 x^2}{125}-\frac{72 x^3}{25}+\frac{1331}{3125 (3+5 x)^2}+\frac{1452}{625 (3+5 x)}\right ) \, dx\\ &=-\frac{1179 x}{3125}-\frac{427 x^2}{625}+\frac{164 x^3}{125}-\frac{18 x^4}{25}-\frac{1331}{15625 (3+5 x)}+\frac{1452 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0281367, size = 51, normalized size = 1.06 \[ \frac{-11250 x^5+13750 x^4+1625 x^3-12300 x^2+2655 x+1452 (5 x+3) \log (6 (5 x+3))+3449}{3125 (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 37, normalized size = 0.8 \begin{align*} -{\frac{1179\,x}{3125}}-{\frac{427\,{x}^{2}}{625}}+{\frac{164\,{x}^{3}}{125}}-{\frac{18\,{x}^{4}}{25}}-{\frac{1331}{46875+78125\,x}}+{\frac{1452\,\ln \left ( 3+5\,x \right ) }{3125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05051, size = 49, normalized size = 1.02 \begin{align*} -\frac{18}{25} \, x^{4} + \frac{164}{125} \, x^{3} - \frac{427}{625} \, x^{2} - \frac{1179}{3125} \, x - \frac{1331}{15625 \,{\left (5 \, x + 3\right )}} + \frac{1452}{3125} \, \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 = 1.31343, size = 154, normalized size = 3.21 \begin{align*} -\frac{56250 \, x^{5} - 68750 \, x^{4} - 8125 \, x^{3} + 61500 \, x^{2} - 7260 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 17685 \, x + 1331}{15625 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.105874, size = 41, normalized size = 0.85 \begin{align*} - \frac{18 x^{4}}{25} + \frac{164 x^{3}}{125} - \frac{427 x^{2}}{625} - \frac{1179 x}{3125} + \frac{1452 \log{\left (5 x + 3 \right )}}{3125} - \frac{1331}{78125 x + 46875} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.99748, size = 89, normalized size = 1.85 \begin{align*} \frac{1}{15625} \,{\left (5 \, x + 3\right )}^{4}{\left (\frac{380}{5 \, x + 3} - \frac{2875}{{\left (5 \, x + 3\right )}^{2}} + \frac{7755}{{\left (5 \, x + 3\right )}^{3}} - 18\right )} - \frac{1331}{15625 \,{\left (5 \, x + 3\right )}} - \frac{1452}{3125} \, \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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