Optimal. Leaf size=51 \[ \frac{81 x^3}{20}+\frac{567 x^2}{25}+\frac{152793 x}{2000}+\frac{16807}{352 (1-2 x)}+\frac{156065 \log (1-2 x)}{1936}+\frac{\log (5 x+3)}{75625} \]
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Rubi [A] time = 0.0247458, antiderivative size = 51, 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} \[ \frac{81 x^3}{20}+\frac{567 x^2}{25}+\frac{152793 x}{2000}+\frac{16807}{352 (1-2 x)}+\frac{156065 \log (1-2 x)}{1936}+\frac{\log (5 x+3)}{75625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac{152793}{2000}+\frac{1134 x}{25}+\frac{243 x^2}{20}+\frac{16807}{176 (-1+2 x)^2}+\frac{156065}{968 (-1+2 x)}+\frac{1}{15125 (3+5 x)}\right ) \, dx\\ &=\frac{16807}{352 (1-2 x)}+\frac{152793 x}{2000}+\frac{567 x^2}{25}+\frac{81 x^3}{20}+\frac{156065 \log (1-2 x)}{1936}+\frac{\log (3+5 x)}{75625}\\ \end{align*}
Mathematica [A] time = 0.0238067, size = 52, normalized size = 1.02 \[ \frac{81 x^3}{20}+\frac{567 x^2}{25}+\frac{152793 x}{2000}+\frac{16807}{352-704 x}+\frac{156065 \log (5-10 x)}{1936}+\frac{\log (5 x+3)}{75625}+\frac{385479}{10000} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 40, normalized size = 0.8 \begin{align*}{\frac{81\,{x}^{3}}{20}}+{\frac{567\,{x}^{2}}{25}}+{\frac{152793\,x}{2000}}-{\frac{16807}{704\,x-352}}+{\frac{156065\,\ln \left ( 2\,x-1 \right ) }{1936}}+{\frac{\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 = 1.33902, size = 53, normalized size = 1.04 \begin{align*} \frac{81}{20} \, x^{3} + \frac{567}{25} \, x^{2} + \frac{152793}{2000} \, x - \frac{16807}{352 \,{\left (2 \, x - 1\right )}} + \frac{1}{75625} \, \log \left (5 \, x + 3\right ) + \frac{156065}{1936} \, \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 = 1.32327, size = 211, normalized size = 4.14 \begin{align*} \frac{19602000 \, x^{4} + 99970200 \, x^{3} + 314873460 \, x^{2} + 32 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 195081250 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 184879530 \, x - 115548125}{2420000 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.134243, size = 42, normalized size = 0.82 \begin{align*} \frac{81 x^{3}}{20} + \frac{567 x^{2}}{25} + \frac{152793 x}{2000} + \frac{156065 \log{\left (x - \frac{1}{2} \right )}}{1936} + \frac{\log{\left (x + \frac{3}{5} \right )}}{75625} - \frac{16807}{704 x - 352} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.24423, size = 97, normalized size = 1.9 \begin{align*} \frac{27}{4000} \,{\left (2 \, x - 1\right )}^{3}{\left (\frac{1065}{2 \, x - 1} + \frac{7564}{{\left (2 \, x - 1\right )}^{2}} + 75\right )} - \frac{16807}{352 \,{\left (2 \, x - 1\right )}} - \frac{806121}{10000} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{75625} \, \log \left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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