Optimal. Leaf size=33 \[ -\frac{125 x^2}{12}-\frac{1225 x}{36}-\frac{1331}{56} \log (1-2 x)-\frac{1}{189} \log (3 x+2) \]
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Rubi [A] time = 0.0132522, antiderivative size = 33, 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 = {72} \[ -\frac{125 x^2}{12}-\frac{1225 x}{36}-\frac{1331}{56} \log (1-2 x)-\frac{1}{189} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)} \, dx &=\int \left (-\frac{1225}{36}-\frac{125 x}{6}-\frac{1331}{28 (-1+2 x)}-\frac{1}{63 (2+3 x)}\right ) \, dx\\ &=-\frac{1225 x}{36}-\frac{125 x^2}{12}-\frac{1331}{56} \log (1-2 x)-\frac{1}{189} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.014913, size = 35, normalized size = 1.06 \[ \frac{-1050 \left (15 x^2+49 x+24\right )-35937 \log (5-10 x)-8 \log (5 (3 x+2))}{1512} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 26, normalized size = 0.8 \begin{align*} -{\frac{125\,{x}^{2}}{12}}-{\frac{1225\,x}{36}}-{\frac{1331\,\ln \left ( 2\,x-1 \right ) }{56}}-{\frac{\ln \left ( 2+3\,x \right ) }{189}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10596, size = 34, normalized size = 1.03 \begin{align*} -\frac{125}{12} \, x^{2} - \frac{1225}{36} \, x - \frac{1}{189} \, \log \left (3 \, x + 2\right ) - \frac{1331}{56} \, \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 = 1.26176, size = 93, normalized size = 2.82 \begin{align*} -\frac{125}{12} \, x^{2} - \frac{1225}{36} \, x - \frac{1}{189} \, \log \left (3 \, x + 2\right ) - \frac{1331}{56} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.121128, size = 31, normalized size = 0.94 \begin{align*} - \frac{125 x^{2}}{12} - \frac{1225 x}{36} - \frac{1331 \log{\left (x - \frac{1}{2} \right )}}{56} - \frac{\log{\left (x + \frac{2}{3} \right )}}{189} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.48798, size = 36, normalized size = 1.09 \begin{align*} -\frac{125}{12} \, x^{2} - \frac{1225}{36} \, x - \frac{1}{189} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{1331}{56} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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