Optimal. Leaf size=65 \[ -\frac{243 x^8}{5}-\frac{11988 x^7}{175}+\frac{4419 x^6}{125}+\frac{243333 x^5}{3125}-\frac{73749 x^4}{12500}-\frac{1703753 x^3}{46875}-\frac{138741 x^2}{156250}+\frac{4166223 x}{390625}+\frac{1331 \log (5 x+3)}{1953125} \]
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Rubi [A] time = 0.0286008, 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} \[ -\frac{243 x^8}{5}-\frac{11988 x^7}{175}+\frac{4419 x^6}{125}+\frac{243333 x^5}{3125}-\frac{73749 x^4}{12500}-\frac{1703753 x^3}{46875}-\frac{138741 x^2}{156250}+\frac{4166223 x}{390625}+\frac{1331 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)^5}{3+5 x} \, dx &=\int \left (\frac{4166223}{390625}-\frac{138741 x}{78125}-\frac{1703753 x^2}{15625}-\frac{73749 x^3}{3125}+\frac{243333 x^4}{625}+\frac{26514 x^5}{125}-\frac{11988 x^6}{25}-\frac{1944 x^7}{5}+\frac{1331}{390625 (3+5 x)}\right ) \, dx\\ &=\frac{4166223 x}{390625}-\frac{138741 x^2}{156250}-\frac{1703753 x^3}{46875}-\frac{73749 x^4}{12500}+\frac{243333 x^5}{3125}+\frac{4419 x^6}{125}-\frac{11988 x^7}{175}-\frac{243 x^8}{5}+\frac{1331 \log (3+5 x)}{1953125}\\ \end{align*}
Mathematica [A] time = 0.0131316, size = 52, normalized size = 0.8 \[ \frac{-39867187500 x^8-56193750000 x^7+28999687500 x^6+63874912500 x^5-4839778125 x^4-29815677500 x^3-728390250 x^2+8749068300 x+559020 \log (5 x+3)+2409164451}{820312500} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 48, normalized size = 0.7 \begin{align*}{\frac{4166223\,x}{390625}}-{\frac{138741\,{x}^{2}}{156250}}-{\frac{1703753\,{x}^{3}}{46875}}-{\frac{73749\,{x}^{4}}{12500}}+{\frac{243333\,{x}^{5}}{3125}}+{\frac{4419\,{x}^{6}}{125}}-{\frac{11988\,{x}^{7}}{175}}-{\frac{243\,{x}^{8}}{5}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{1953125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03861, size = 63, normalized size = 0.97 \begin{align*} -\frac{243}{5} \, x^{8} - \frac{11988}{175} \, x^{7} + \frac{4419}{125} \, x^{6} + \frac{243333}{3125} \, x^{5} - \frac{73749}{12500} \, x^{4} - \frac{1703753}{46875} \, x^{3} - \frac{138741}{156250} \, x^{2} + \frac{4166223}{390625} \, x + \frac{1331}{1953125} \, \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 = 1.51544, size = 224, normalized size = 3.45 \begin{align*} -\frac{243}{5} \, x^{8} - \frac{11988}{175} \, x^{7} + \frac{4419}{125} \, x^{6} + \frac{243333}{3125} \, x^{5} - \frac{73749}{12500} \, x^{4} - \frac{1703753}{46875} \, x^{3} - \frac{138741}{156250} \, x^{2} + \frac{4166223}{390625} \, x + \frac{1331}{1953125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.097946, size = 61, normalized size = 0.94 \begin{align*} - \frac{243 x^{8}}{5} - \frac{11988 x^{7}}{175} + \frac{4419 x^{6}}{125} + \frac{243333 x^{5}}{3125} - \frac{73749 x^{4}}{12500} - \frac{1703753 x^{3}}{46875} - \frac{138741 x^{2}}{156250} + \frac{4166223 x}{390625} + \frac{1331 \log{\left (5 x + 3 \right )}}{1953125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.08662, size = 65, normalized size = 1. \begin{align*} -\frac{243}{5} \, x^{8} - \frac{11988}{175} \, x^{7} + \frac{4419}{125} \, x^{6} + \frac{243333}{3125} \, x^{5} - \frac{73749}{12500} \, x^{4} - \frac{1703753}{46875} \, x^{3} - \frac{138741}{156250} \, x^{2} + \frac{4166223}{390625} \, x + \frac{1331}{1953125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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