Optimal. Leaf size=72 \[ -\frac{648 x^9}{5}-\frac{13851 x^8}{50}-\frac{40338 x^7}{875}+\frac{331713 x^6}{1250}+\frac{2212083 x^5}{15625}-\frac{5848749 x^4}{62500}-\frac{17453753 x^3}{234375}+\frac{11111259 x^2}{781250}+\frac{41666223 x}{1953125}+\frac{1331 \log (5 x+3)}{9765625} \]
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Rubi [A] time = 0.0310059, antiderivative size = 72, 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} \[ -\frac{648 x^9}{5}-\frac{13851 x^8}{50}-\frac{40338 x^7}{875}+\frac{331713 x^6}{1250}+\frac{2212083 x^5}{15625}-\frac{5848749 x^4}{62500}-\frac{17453753 x^3}{234375}+\frac{11111259 x^2}{781250}+\frac{41666223 x}{1953125}+\frac{1331 \log (5 x+3)}{9765625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)^6}{3+5 x} \, dx &=\int \left (\frac{41666223}{1953125}+\frac{11111259 x}{390625}-\frac{17453753 x^2}{78125}-\frac{5848749 x^3}{15625}+\frac{2212083 x^4}{3125}+\frac{995139 x^5}{625}-\frac{40338 x^6}{125}-\frac{55404 x^7}{25}-\frac{5832 x^8}{5}+\frac{1331}{1953125 (3+5 x)}\right ) \, dx\\ &=\frac{41666223 x}{1953125}+\frac{11111259 x^2}{781250}-\frac{17453753 x^3}{234375}-\frac{5848749 x^4}{62500}+\frac{2212083 x^5}{15625}+\frac{331713 x^6}{1250}-\frac{40338 x^7}{875}-\frac{13851 x^8}{50}-\frac{648 x^9}{5}+\frac{1331 \log (3+5 x)}{9765625}\\ \end{align*}
Mathematica [A] time = 0.0143477, size = 57, normalized size = 0.79 \[ \frac{-531562500000 x^9-1136214843750 x^8-189084375000 x^7+1088433281250 x^6+580671787500 x^5-383824153125 x^4-305440677500 x^3+58334109750 x^2+87499068300 x+559020 \log (5 x+3)+18072649071}{4101562500} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 53, normalized size = 0.7 \begin{align*}{\frac{41666223\,x}{1953125}}+{\frac{11111259\,{x}^{2}}{781250}}-{\frac{17453753\,{x}^{3}}{234375}}-{\frac{5848749\,{x}^{4}}{62500}}+{\frac{2212083\,{x}^{5}}{15625}}+{\frac{331713\,{x}^{6}}{1250}}-{\frac{40338\,{x}^{7}}{875}}-{\frac{13851\,{x}^{8}}{50}}-{\frac{648\,{x}^{9}}{5}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{9765625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03831, size = 70, normalized size = 0.97 \begin{align*} -\frac{648}{5} \, x^{9} - \frac{13851}{50} \, x^{8} - \frac{40338}{875} \, x^{7} + \frac{331713}{1250} \, x^{6} + \frac{2212083}{15625} \, x^{5} - \frac{5848749}{62500} \, x^{4} - \frac{17453753}{234375} \, x^{3} + \frac{11111259}{781250} \, x^{2} + \frac{41666223}{1953125} \, x + \frac{1331}{9765625} \, \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 = 1.43231, size = 262, normalized size = 3.64 \begin{align*} -\frac{648}{5} \, x^{9} - \frac{13851}{50} \, x^{8} - \frac{40338}{875} \, x^{7} + \frac{331713}{1250} \, x^{6} + \frac{2212083}{15625} \, x^{5} - \frac{5848749}{62500} \, x^{4} - \frac{17453753}{234375} \, x^{3} + \frac{11111259}{781250} \, x^{2} + \frac{41666223}{1953125} \, x + \frac{1331}{9765625} \, \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 = 0.099135, size = 68, normalized size = 0.94 \begin{align*} - \frac{648 x^{9}}{5} - \frac{13851 x^{8}}{50} - \frac{40338 x^{7}}{875} + \frac{331713 x^{6}}{1250} + \frac{2212083 x^{5}}{15625} - \frac{5848749 x^{4}}{62500} - \frac{17453753 x^{3}}{234375} + \frac{11111259 x^{2}}{781250} + \frac{41666223 x}{1953125} + \frac{1331 \log{\left (5 x + 3 \right )}}{9765625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.35695, size = 72, normalized size = 1. \begin{align*} -\frac{648}{5} \, x^{9} - \frac{13851}{50} \, x^{8} - \frac{40338}{875} \, x^{7} + \frac{331713}{1250} \, x^{6} + \frac{2212083}{15625} \, x^{5} - \frac{5848749}{62500} \, x^{4} - \frac{17453753}{234375} \, x^{3} + \frac{11111259}{781250} \, x^{2} + \frac{41666223}{1953125} \, x + \frac{1331}{9765625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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