Optimal. Leaf size=43 \[ \frac{1}{121 (1-2 x)}+\frac{7}{44 (1-2 x)^2}-\frac{5 \log (1-2 x)}{1331}+\frac{5 \log (5 x+3)}{1331} \]
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Rubi [A] time = 0.015923, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{1}{121 (1-2 x)}+\frac{7}{44 (1-2 x)^2}-\frac{5 \log (1-2 x)}{1331}+\frac{5 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{2+3 x}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac{7}{11 (-1+2 x)^3}+\frac{2}{121 (-1+2 x)^2}-\frac{10}{1331 (-1+2 x)}+\frac{25}{1331 (3+5 x)}\right ) \, dx\\ &=\frac{7}{44 (1-2 x)^2}+\frac{1}{121 (1-2 x)}-\frac{5 \log (1-2 x)}{1331}+\frac{5 \log (3+5 x)}{1331}\\ \end{align*}
Mathematica [A] time = 0.0148925, size = 46, normalized size = 1.07 \[ \frac{-88 x-20 (1-2 x)^2 \log (1-2 x)+20 (1-2 x)^2 \log (10 x+6)+891}{5324 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*}{\frac{7}{44\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{1}{242\,x-121}}-{\frac{5\,\ln \left ( 2\,x-1 \right ) }{1331}}+{\frac{5\,\ln \left ( 3+5\,x \right ) }{1331}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13342, size = 49, normalized size = 1.14 \begin{align*} -\frac{8 \, x - 81}{484 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{5}{1331} \, \log \left (5 \, x + 3\right ) - \frac{5}{1331} \, \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 = 1.60221, size = 150, normalized size = 3.49 \begin{align*} \frac{20 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 20 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 88 \, x + 891}{5324 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.130404, size = 34, normalized size = 0.79 \begin{align*} - \frac{8 x - 81}{1936 x^{2} - 1936 x + 484} - \frac{5 \log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{5 \log{\left (x + \frac{3}{5} \right )}}{1331} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.10754, size = 45, normalized size = 1.05 \begin{align*} -\frac{8 \, x - 81}{484 \,{\left (2 \, x - 1\right )}^{2}} + \frac{5}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{5}{1331} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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