Optimal. Leaf size=44 \[ -\frac {162 x^5}{25}-\frac {1269 x^4}{100}-\frac {531 x^3}{125}+\frac {7779 x^2}{1250}+\frac {16663 x}{3125}+\frac {11 \log (5 x+3)}{15625} \]
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Rubi [A] time = 0.02, antiderivative size = 44, 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} \[ -\frac {162 x^5}{25}-\frac {1269 x^4}{100}-\frac {531 x^3}{125}+\frac {7779 x^2}{1250}+\frac {16663 x}{3125}+\frac {11 \log (5 x+3)}{15625} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^4}{3+5 x} \, dx &=\int \left (\frac {16663}{3125}+\frac {7779 x}{625}-\frac {1593 x^2}{125}-\frac {1269 x^3}{25}-\frac {162 x^4}{5}+\frac {11}{3125 (3+5 x)}\right ) \, dx\\ &=\frac {16663 x}{3125}+\frac {7779 x^2}{1250}-\frac {531 x^3}{125}-\frac {1269 x^4}{100}-\frac {162 x^5}{25}+\frac {11 \log (3+5 x)}{15625}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 37, normalized size = 0.84 \[ \frac {-2025000 x^5-3965625 x^4-1327500 x^3+1944750 x^2+1666300 x+220 \log (5 x+3)+369411}{312500} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 32, normalized size = 0.73 \[ -\frac {162}{25} \, x^{5} - \frac {1269}{100} \, x^{4} - \frac {531}{125} \, x^{3} + \frac {7779}{1250} \, x^{2} + \frac {16663}{3125} \, x + \frac {11}{15625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 33, normalized size = 0.75 \[ -\frac {162}{25} \, x^{5} - \frac {1269}{100} \, x^{4} - \frac {531}{125} \, x^{3} + \frac {7779}{1250} \, x^{2} + \frac {16663}{3125} \, x + \frac {11}{15625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 33, normalized size = 0.75 \[ -\frac {162 x^{5}}{25}-\frac {1269 x^{4}}{100}-\frac {531 x^{3}}{125}+\frac {7779 x^{2}}{1250}+\frac {16663 x}{3125}+\frac {11 \ln \left (5 x +3\right )}{15625} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 32, normalized size = 0.73 \[ -\frac {162}{25} \, x^{5} - \frac {1269}{100} \, x^{4} - \frac {531}{125} \, x^{3} + \frac {7779}{1250} \, x^{2} + \frac {16663}{3125} \, x + \frac {11}{15625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 30, normalized size = 0.68 \[ \frac {16663\,x}{3125}+\frac {11\,\ln \left (x+\frac {3}{5}\right )}{15625}+\frac {7779\,x^2}{1250}-\frac {531\,x^3}{125}-\frac {1269\,x^4}{100}-\frac {162\,x^5}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 41, normalized size = 0.93 \[ - \frac {162 x^{5}}{25} - \frac {1269 x^{4}}{100} - \frac {531 x^{3}}{125} + \frac {7779 x^{2}}{1250} + \frac {16663 x}{3125} + \frac {11 \log {\left (5 x + 3 \right )}}{15625} \]
Verification of antiderivative is not currently implemented for this CAS.
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