Optimal. Leaf size=40 \[ -\frac {27 x^3}{10}-\frac {2079 x^2}{200}-\frac {21951 x}{1000}-\frac {2401}{176} \log (1-2 x)+\frac {\log (5 x+3)}{6875} \]
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Rubi [A] time = 0.02, antiderivative size = 40, 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} \[ -\frac {27 x^3}{10}-\frac {2079 x^2}{200}-\frac {21951 x}{1000}-\frac {2401}{176} \log (1-2 x)+\frac {\log (5 x+3)}{6875} \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac {21951}{1000}-\frac {2079 x}{100}-\frac {81 x^2}{10}-\frac {2401}{88 (-1+2 x)}+\frac {1}{1375 (3+5 x)}\right ) \, dx\\ &=-\frac {21951 x}{1000}-\frac {2079 x^2}{200}-\frac {27 x^3}{10}-\frac {2401}{176} \log (1-2 x)+\frac {\log (3+5 x)}{6875}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 43, normalized size = 1.08 \[ \frac {8 \log (-3 (5 x+3))-55 \left (2700 x^3+10395 x^2+21951 x+10814\right )}{55000}-\frac {2401}{176} \log (3-6 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 30, normalized size = 0.75 \[ -\frac {27}{10} \, x^{3} - \frac {2079}{200} \, x^{2} - \frac {21951}{1000} \, x + \frac {1}{6875} \, \log \left (5 \, x + 3\right ) - \frac {2401}{176} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 32, normalized size = 0.80 \[ -\frac {27}{10} \, x^{3} - \frac {2079}{200} \, x^{2} - \frac {21951}{1000} \, x + \frac {1}{6875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {2401}{176} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 31, normalized size = 0.78 \[ -\frac {27 x^{3}}{10}-\frac {2079 x^{2}}{200}-\frac {21951 x}{1000}-\frac {2401 \ln \left (2 x -1\right )}{176}+\frac {\ln \left (5 x +3\right )}{6875} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 30, normalized size = 0.75 \[ -\frac {27}{10} \, x^{3} - \frac {2079}{200} \, x^{2} - \frac {21951}{1000} \, x + \frac {1}{6875} \, \log \left (5 \, x + 3\right ) - \frac {2401}{176} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 26, normalized size = 0.65 \[ \frac {\ln \left (x+\frac {3}{5}\right )}{6875}-\frac {2401\,\ln \left (x-\frac {1}{2}\right )}{176}-\frac {21951\,x}{1000}-\frac {2079\,x^2}{200}-\frac {27\,x^3}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 36, normalized size = 0.90 \[ - \frac {27 x^{3}}{10} - \frac {2079 x^{2}}{200} - \frac {21951 x}{1000} - \frac {2401 \log {\left (x - \frac {1}{2} \right )}}{176} + \frac {\log {\left (x + \frac {3}{5} \right )}}{6875} \]
Verification of antiderivative is not currently implemented for this CAS.
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