Optimal. Leaf size=33 \[ -\frac {27 x^2}{20}-\frac {513 x}{100}-\frac {343}{88} \log (1-2 x)+\frac {\log (5 x+3)}{1375} \]
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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} \[ -\frac {27 x^2}{20}-\frac {513 x}{100}-\frac {343}{88} \log (1-2 x)+\frac {\log (5 x+3)}{1375} \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac {513}{100}-\frac {27 x}{10}-\frac {343}{44 (-1+2 x)}+\frac {1}{275 (3+5 x)}\right ) \, dx\\ &=-\frac {513 x}{100}-\frac {27 x^2}{20}-\frac {343}{88} \log (1-2 x)+\frac {\log (3+5 x)}{1375}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 35, normalized size = 1.06 \[ \frac {-330 \left (45 x^2+171 x+94\right )-42875 \log (3-6 x)+8 \log (-3 (5 x+3))}{11000} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 25, normalized size = 0.76 \[ -\frac {27}{20} \, x^{2} - \frac {513}{100} \, x + \frac {1}{1375} \, \log \left (5 \, x + 3\right ) - \frac {343}{88} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 27, normalized size = 0.82 \[ -\frac {27}{20} \, x^{2} - \frac {513}{100} \, x + \frac {1}{1375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {343}{88} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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 \[ -\frac {27 x^{2}}{20}-\frac {513 x}{100}-\frac {343 \ln \left (2 x -1\right )}{88}+\frac {\ln \left (5 x +3\right )}{1375} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 25, normalized size = 0.76 \[ -\frac {27}{20} \, x^{2} - \frac {513}{100} \, x + \frac {1}{1375} \, \log \left (5 \, x + 3\right ) - \frac {343}{88} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 21, normalized size = 0.64 \[ \frac {\ln \left (x+\frac {3}{5}\right )}{1375}-\frac {343\,\ln \left (x-\frac {1}{2}\right )}{88}-\frac {513\,x}{100}-\frac {27\,x^2}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 29, normalized size = 0.88 \[ - \frac {27 x^{2}}{20} - \frac {513 x}{100} - \frac {343 \log {\left (x - \frac {1}{2} \right )}}{88} + \frac {\log {\left (x + \frac {3}{5} \right )}}{1375} \]
Verification of antiderivative is not currently implemented for this CAS.
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