Optimal. Leaf size=30 \[ \frac {43 x}{125}-\frac {28 x^2}{25}+\frac {4 x^3}{5}+\frac {121}{625} \log (3+5 x) \]
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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 {4 x^3}{5}-\frac {28 x^2}{25}+\frac {43 x}{125}+\frac {121}{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 (2+3 x)}{3+5 x} \, dx &=\int \left (\frac {43}{125}-\frac {56 x}{25}+\frac {12 x^2}{5}+\frac {121}{125 (3+5 x)}\right ) \, dx\\ &=\frac {43 x}{125}-\frac {28 x^2}{25}+\frac {4 x^3}{5}+\frac {121}{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 {1}{625} \left (489+215 x-700 x^2+500 x^3+121 \log (3+5 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 23, normalized size = 0.77
method | result | size |
default | \(\frac {43 x}{125}-\frac {28 x^{2}}{25}+\frac {4 x^{3}}{5}+\frac {121 \ln \left (3+5 x \right )}{625}\) | \(23\) |
norman | \(\frac {43 x}{125}-\frac {28 x^{2}}{25}+\frac {4 x^{3}}{5}+\frac {121 \ln \left (3+5 x \right )}{625}\) | \(23\) |
risch | \(\frac {43 x}{125}-\frac {28 x^{2}}{25}+\frac {4 x^{3}}{5}+\frac {121 \ln \left (3+5 x \right )}{625}\) | \(23\) |
meijerg | \(\frac {121 \ln \left (1+\frac {5 x}{3}\right )}{625}-x +\frac {2 x \left (-5 x +6\right )}{25}+\frac {9 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 22, normalized size = 0.73 \begin {gather*} \frac {4}{5} \, x^{3} - \frac {28}{25} \, x^{2} + \frac {43}{125} \, x + \frac {121}{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 = 0.41, size = 22, normalized size = 0.73 \begin {gather*} \frac {4}{5} \, x^{3} - \frac {28}{25} \, x^{2} + \frac {43}{125} \, x + \frac {121}{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 = 0.03, size = 27, normalized size = 0.90 \begin {gather*} \frac {4 x^{3}}{5} - \frac {28 x^{2}}{25} + \frac {43 x}{125} + \frac {121 \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 = 1.37, size = 23, normalized size = 0.77 \begin {gather*} \frac {4}{5} \, x^{3} - \frac {28}{25} \, x^{2} + \frac {43}{125} \, x + \frac {121}{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 {43\,x}{125}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {28\,x^2}{25}+\frac {4\,x^3}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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