Optimal. Leaf size=43 \[ -\frac{7}{121 (5 x+3)}-\frac{1}{110 (5 x+3)^2}-\frac{14 \log (1-2 x)}{1331}+\frac{14 \log (5 x+3)}{1331} \]
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Rubi [A] time = 0.0157576, 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} \[ -\frac{7}{121 (5 x+3)}-\frac{1}{110 (5 x+3)^2}-\frac{14 \log (1-2 x)}{1331}+\frac{14 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{2+3 x}{(1-2 x) (3+5 x)^3} \, dx &=\int \left (-\frac{28}{1331 (-1+2 x)}+\frac{1}{11 (3+5 x)^3}+\frac{35}{121 (3+5 x)^2}+\frac{70}{1331 (3+5 x)}\right ) \, dx\\ &=-\frac{1}{110 (3+5 x)^2}-\frac{7}{121 (3+5 x)}-\frac{14 \log (1-2 x)}{1331}+\frac{14 \log (3+5 x)}{1331}\\ \end{align*}
Mathematica [A] time = 0.018053, size = 35, normalized size = 0.81 \[ \frac{-\frac{11 (350 x+221)}{(5 x+3)^2}-140 \log (5-10 x)+140 \log (5 x+3)}{13310} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{14\,\ln \left ( 2\,x-1 \right ) }{1331}}-{\frac{1}{110\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{7}{363+605\,x}}+{\frac{14\,\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 = 1.20983, size = 49, normalized size = 1.14 \begin{align*} -\frac{350 \, x + 221}{1210 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{14}{1331} \, \log \left (5 \, x + 3\right ) - \frac{14}{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 = 1.31476, size = 166, normalized size = 3.86 \begin{align*} \frac{140 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 140 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 3850 \, x - 2431}{13310 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.135476, size = 34, normalized size = 0.79 \begin{align*} - \frac{350 x + 221}{30250 x^{2} + 36300 x + 10890} - \frac{14 \log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{14 \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 = 1.2838, size = 45, normalized size = 1.05 \begin{align*} -\frac{350 \, x + 221}{1210 \,{\left (5 \, x + 3\right )}^{2}} + \frac{14}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{14}{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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