Optimal. Leaf size=59 \[ -\frac{243 x}{200}-\frac{228095}{21296 (1-2 x)}-\frac{1}{166375 (5 x+3)}+\frac{16807}{3872 (1-2 x)^2}-\frac{1034145 \log (1-2 x)}{234256}+\frac{171 \log (5 x+3)}{1830125} \]
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Rubi [A] time = 0.0266856, antiderivative size = 59, 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} \[ -\frac{243 x}{200}-\frac{228095}{21296 (1-2 x)}-\frac{1}{166375 (5 x+3)}+\frac{16807}{3872 (1-2 x)^2}-\frac{1034145 \log (1-2 x)}{234256}+\frac{171 \log (5 x+3)}{1830125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)^2} \, dx &=\int \left (-\frac{243}{200}-\frac{16807}{968 (-1+2 x)^3}-\frac{228095}{10648 (-1+2 x)^2}-\frac{1034145}{117128 (-1+2 x)}+\frac{1}{33275 (3+5 x)^2}+\frac{171}{366025 (3+5 x)}\right ) \, dx\\ &=\frac{16807}{3872 (1-2 x)^2}-\frac{228095}{21296 (1-2 x)}-\frac{243 x}{200}-\frac{1}{166375 (3+5 x)}-\frac{1034145 \log (1-2 x)}{234256}+\frac{171 \log (3+5 x)}{1830125}\\ \end{align*}
Mathematica [A] time = 0.0351674, size = 55, normalized size = 0.93 \[ \frac{35577630 (1-2 x)+\frac{627261250}{2 x-1}-\frac{352}{5 x+3}+\frac{254205875}{(1-2 x)^2}-258536250 \log (1-2 x)+5472 \log (10 x+6)}{58564000} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 48, normalized size = 0.8 \begin{align*} -{\frac{243\,x}{200}}+{\frac{16807}{3872\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{228095}{42592\,x-21296}}-{\frac{1034145\,\ln \left ( 2\,x-1 \right ) }{234256}}-{\frac{1}{499125+831875\,x}}+{\frac{171\,\ln \left ( 3+5\,x \right ) }{1830125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06381, size = 66, normalized size = 1.12 \begin{align*} -\frac{243}{200} \, x + \frac{570237372 \, x^{2} + 172572003 \, x - 101742407}{5324000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{171}{1830125} \, \log \left (5 \, x + 3\right ) - \frac{1034145}{234256} \, \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 = 1.47731, size = 293, normalized size = 4.97 \begin{align*} -\frac{1423105200 \, x^{4} - 569242080 \, x^{3} - 6770697912 \, x^{2} - 5472 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 258536250 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 1684826253 \, x + 1119166477}{58564000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.183134, size = 49, normalized size = 0.83 \begin{align*} - \frac{243 x}{200} + \frac{570237372 x^{2} + 172572003 x - 101742407}{106480000 x^{3} - 42592000 x^{2} - 37268000 x + 15972000} - \frac{1034145 \log{\left (x - \frac{1}{2} \right )}}{234256} + \frac{171 \log{\left (x + \frac{3}{5} \right )}}{1830125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 4.53909, size = 112, normalized size = 1.9 \begin{align*} \frac{{\left (5 \, x + 3\right )}{\left (\frac{389138447}{5 \, x + 3} - \frac{1420901823}{{\left (5 \, x + 3\right )}^{2}} - 14231052\right )}}{14641000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{1}{166375 \,{\left (5 \, x + 3\right )}} + \frac{8829}{2000} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{1034145}{234256} \, \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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