Optimal. Leaf size=37 \[ -\frac {6 x^4}{5}+\frac {172 x^3}{75}-\frac {183 x^2}{125}-\frac {27 x}{625}+\frac {1331 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {6 x^4}{5}+\frac {172 x^3}{75}-\frac {183 x^2}{125}-\frac {27 x}{625}+\frac {1331 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx &=\int \left (-\frac {27}{625}-\frac {366 x}{125}+\frac {172 x^2}{25}-\frac {24 x^3}{5}+\frac {1331}{625 (3+5 x)}\right ) \, dx\\ &=-\frac {27 x}{625}-\frac {183 x^2}{125}+\frac {172 x^3}{75}-\frac {6 x^4}{5}+\frac {1331 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 35, normalized size = 0.95 \[ \frac {3993 \log (5 x+3)-5 \left (2250 x^4-4300 x^3+2745 x^2+81 x-2160\right )}{9375} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 27, normalized size = 0.73 \[ -\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 28, normalized size = 0.76 \[ -\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 28, normalized size = 0.76 \[ -\frac {6 x^{4}}{5}+\frac {172 x^{3}}{75}-\frac {183 x^{2}}{125}-\frac {27 x}{625}+\frac {1331 \ln \left (5 x +3\right )}{3125} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 27, normalized size = 0.73 \[ -\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 25, normalized size = 0.68 \[ \frac {1331\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {27\,x}{625}-\frac {183\,x^2}{125}+\frac {172\,x^3}{75}-\frac {6\,x^4}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 34, normalized size = 0.92 \[ - \frac {6 x^{4}}{5} + \frac {172 x^{3}}{75} - \frac {183 x^{2}}{125} - \frac {27 x}{625} + \frac {1331 \log {\left (5 x + 3 \right )}}{3125} \]
Verification of antiderivative is not currently implemented for this CAS.
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