Optimal. Leaf size=30 \[ \frac {163 x}{125}-\frac {21 x^2}{50}-\frac {6 x^3}{5}+\frac {11}{625} \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 30, 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 {6 x^3}{5}-\frac {21 x^2}{50}+\frac {163 x}{125}+\frac {11}{625} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^2}{3+5 x} \, dx &=\int \left (\frac {163}{125}-\frac {21 x}{25}-\frac {18 x^2}{5}+\frac {11}{125 (3+5 x)}\right ) \, dx\\ &=\frac {163 x}{125}-\frac {21 x^2}{50}-\frac {6 x^3}{5}+\frac {11}{625} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 0.90 \begin {gather*} \frac {843+1630 x-525 x^2-1500 x^3+22 \log (3+5 x)}{1250} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 23, normalized size = 0.77
method | result | size |
default | \(\frac {163 x}{125}-\frac {21 x^{2}}{50}-\frac {6 x^{3}}{5}+\frac {11 \ln \left (3+5 x \right )}{625}\) | \(23\) |
norman | \(\frac {163 x}{125}-\frac {21 x^{2}}{50}-\frac {6 x^{3}}{5}+\frac {11 \ln \left (3+5 x \right )}{625}\) | \(23\) |
risch | \(\frac {163 x}{125}-\frac {21 x^{2}}{50}-\frac {6 x^{3}}{5}+\frac {11 \ln \left (3+5 x \right )}{625}\) | \(23\) |
meijerg | \(\frac {11 \ln \left (1+\frac {5 x}{3}\right )}{625}+\frac {4 x}{5}+\frac {3 x \left (-5 x +6\right )}{10}-\frac {27 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{250}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 22, normalized size = 0.73 \begin {gather*} -\frac {6}{5} \, x^{3} - \frac {21}{50} \, x^{2} + \frac {163}{125} \, x + \frac {11}{625} \, \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 = 0.89, size = 22, normalized size = 0.73 \begin {gather*} -\frac {6}{5} \, x^{3} - \frac {21}{50} \, x^{2} + \frac {163}{125} \, x + \frac {11}{625} \, \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 = 0.02, size = 27, normalized size = 0.90 \begin {gather*} - \frac {6 x^{3}}{5} - \frac {21 x^{2}}{50} + \frac {163 x}{125} + \frac {11 \log {\left (5 x + 3 \right )}}{625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.29, size = 23, normalized size = 0.77 \begin {gather*} -\frac {6}{5} \, x^{3} - \frac {21}{50} \, x^{2} + \frac {163}{125} \, x + \frac {11}{625} \, \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 = 0.03, size = 20, normalized size = 0.67 \begin {gather*} \frac {163\,x}{125}+\frac {11\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {21\,x^2}{50}-\frac {6\,x^3}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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