Optimal. Leaf size=44 \[ -\frac{81 x^2}{100}-\frac{1593 x}{500}-\frac{1}{6875 (5 x+3)}-\frac{2401}{968} \log (1-2 x)+\frac{134 \log (5 x+3)}{75625} \]
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Rubi [A] time = 0.0195941, antiderivative size = 44, normalized size of antiderivative = 1., 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 = {88} \[ -\frac{81 x^2}{100}-\frac{1593 x}{500}-\frac{1}{6875 (5 x+3)}-\frac{2401}{968} \log (1-2 x)+\frac{134 \log (5 x+3)}{75625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac{1593}{500}-\frac{81 x}{50}-\frac{2401}{484 (-1+2 x)}+\frac{1}{1375 (3+5 x)^2}+\frac{134}{15125 (3+5 x)}\right ) \, dx\\ &=-\frac{1593 x}{500}-\frac{81 x^2}{100}-\frac{1}{6875 (3+5 x)}-\frac{2401}{968} \log (1-2 x)+\frac{134 \log (3+5 x)}{75625}\\ \end{align*}
Mathematica [A] time = 0.0261691, size = 52, normalized size = 1.18 \[ -\frac{81}{400} (1-2 x)^2+\frac{999}{500} (1-2 x)-\frac{1}{6875 (5 x+3)}-\frac{2401}{968} \log (1-2 x)+\frac{134 \log (10 x+6)}{75625} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 35, normalized size = 0.8 \begin{align*} -{\frac{81\,{x}^{2}}{100}}-{\frac{1593\,x}{500}}-{\frac{2401\,\ln \left ( 2\,x-1 \right ) }{968}}-{\frac{1}{20625+34375\,x}}+{\frac{134\,\ln \left ( 3+5\,x \right ) }{75625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.1068, size = 46, normalized size = 1.05 \begin{align*} -\frac{81}{100} \, x^{2} - \frac{1593}{500} \, x - \frac{1}{6875 \,{\left (5 \, x + 3\right )}} + \frac{134}{75625} \, \log \left (5 \, x + 3\right ) - \frac{2401}{968} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.25154, size = 176, normalized size = 4. \begin{align*} -\frac{2450250 \, x^{3} + 11107800 \, x^{2} - 1072 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 1500625 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 5782590 \, x + 88}{605000 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.144585, size = 37, normalized size = 0.84 \begin{align*} - \frac{81 x^{2}}{100} - \frac{1593 x}{500} - \frac{2401 \log{\left (x - \frac{1}{2} \right )}}{968} + \frac{134 \log{\left (x + \frac{3}{5} \right )}}{75625} - \frac{1}{34375 x + 20625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.34675, size = 85, normalized size = 1.93 \begin{align*} -\frac{27}{2500} \,{\left (5 \, x + 3\right )}^{2}{\left (\frac{41}{5 \, x + 3} + 3\right )} - \frac{1}{6875 \,{\left (5 \, x + 3\right )}} + \frac{12393}{5000} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{2401}{968} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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