Optimal. Leaf size=37 \[ \frac {1663 x}{625}+\frac {279 x^2}{250}-\frac {81 x^3}{25}-\frac {27 x^4}{10}+\frac {11 \log (3+5 x)}{3125} \]
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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 = {78}
\begin {gather*} -\frac {27 x^4}{10}-\frac {81 x^3}{25}+\frac {279 x^2}{250}+\frac {1663 x}{625}+\frac {11 \log (5 x+3)}{3125} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^3}{3+5 x} \, dx &=\int \left (\frac {1663}{625}+\frac {279 x}{125}-\frac {243 x^2}{25}-\frac {54 x^3}{5}+\frac {11}{625 (3+5 x)}\right ) \, dx\\ &=\frac {1663 x}{625}+\frac {279 x^2}{250}-\frac {81 x^3}{25}-\frac {27 x^4}{10}+\frac {11 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 35, normalized size = 0.95 \begin {gather*} \frac {5 \left (1056+3326 x+1395 x^2-4050 x^3-3375 x^4\right )+22 \log (3+5 x)}{6250} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 28, normalized size = 0.76
method | result | size |
default | \(\frac {1663 x}{625}+\frac {279 x^{2}}{250}-\frac {81 x^{3}}{25}-\frac {27 x^{4}}{10}+\frac {11 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
norman | \(\frac {1663 x}{625}+\frac {279 x^{2}}{250}-\frac {81 x^{3}}{25}-\frac {27 x^{4}}{10}+\frac {11 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
risch | \(\frac {1663 x}{625}+\frac {279 x^{2}}{250}-\frac {81 x^{3}}{25}-\frac {27 x^{4}}{10}+\frac {11 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
meijerg | \(\frac {11 \ln \left (1+\frac {5 x}{3}\right )}{3125}+4 x +\frac {9 x \left (-5 x +6\right )}{25}-\frac {243 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{500}+\frac {243 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{6250}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 27, normalized size = 0.73 \begin {gather*} -\frac {27}{10} \, x^{4} - \frac {81}{25} \, x^{3} + \frac {279}{250} \, x^{2} + \frac {1663}{625} \, x + \frac {11}{3125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.33, size = 27, normalized size = 0.73 \begin {gather*} -\frac {27}{10} \, x^{4} - \frac {81}{25} \, x^{3} + \frac {279}{250} \, x^{2} + \frac {1663}{625} \, x + \frac {11}{3125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 34, normalized size = 0.92 \begin {gather*} - \frac {27 x^{4}}{10} - \frac {81 x^{3}}{25} + \frac {279 x^{2}}{250} + \frac {1663 x}{625} + \frac {11 \log {\left (5 x + 3 \right )}}{3125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.86, size = 28, normalized size = 0.76 \begin {gather*} -\frac {27}{10} \, x^{4} - \frac {81}{25} \, x^{3} + \frac {279}{250} \, x^{2} + \frac {1663}{625} \, x + \frac {11}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
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 \begin {gather*} \frac {1663\,x}{625}+\frac {11\,\ln \left (x+\frac {3}{5}\right )}{3125}+\frac {279\,x^2}{250}-\frac {81\,x^3}{25}-\frac {27\,x^4}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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