Optimal. Leaf size=33 \[ -\frac {4 x^2}{15}+\frac {332 x}{225}-\frac {343}{27} \log (3 x+2)+\frac {1331}{125} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {72} \[ -\frac {4 x^2}{15}+\frac {332 x}{225}-\frac {343}{27} \log (3 x+2)+\frac {1331}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x) (3+5 x)} \, dx &=\int \left (\frac {332}{225}-\frac {8 x}{15}-\frac {343}{9 (2+3 x)}+\frac {1331}{25 (3+5 x)}\right ) \, dx\\ &=\frac {332 x}{225}-\frac {4 x^2}{15}-\frac {343}{27} \log (2+3 x)+\frac {1331}{125} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 35, normalized size = 1.06 \[ \frac {60 \left (-15 x^2+83 x+62\right )-42875 \log (3 x+2)+35937 \log (-3 (5 x+3))}{3375} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 25, normalized size = 0.76 \[ -\frac {4}{15} \, x^{2} + \frac {332}{225} \, x + \frac {1331}{125} \, \log \left (5 \, x + 3\right ) - \frac {343}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 27, normalized size = 0.82 \[ -\frac {4}{15} \, x^{2} + \frac {332}{225} \, x + \frac {1331}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {343}{27} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 26, normalized size = 0.79 \[ -\frac {4 x^{2}}{15}+\frac {332 x}{225}-\frac {343 \ln \left (3 x +2\right )}{27}+\frac {1331 \ln \left (5 x +3\right )}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 25, normalized size = 0.76 \[ -\frac {4}{15} \, x^{2} + \frac {332}{225} \, x + \frac {1331}{125} \, \log \left (5 \, x + 3\right ) - \frac {343}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 21, normalized size = 0.64 \[ \frac {332\,x}{225}-\frac {343\,\ln \left (x+\frac {2}{3}\right )}{27}+\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {4\,x^2}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 31, normalized size = 0.94 \[ - \frac {4 x^{2}}{15} + \frac {332 x}{225} + \frac {1331 \log {\left (x + \frac {3}{5} \right )}}{125} - \frac {343 \log {\left (x + \frac {2}{3} \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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