Optimal. Leaf size=43 \[ \frac{4719}{125 (5 x+3)}-\frac{1331}{250 (5 x+3)^2}-\frac{343}{3} \log (3 x+2)+\frac{14289}{125} \log (5 x+3) \]
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Rubi [A] time = 0.0195802, antiderivative size = 43, 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} \[ \frac{4719}{125 (5 x+3)}-\frac{1331}{250 (5 x+3)^2}-\frac{343}{3} \log (3 x+2)+\frac{14289}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)^3} \, dx &=\int \left (-\frac{343}{2+3 x}+\frac{1331}{25 (3+5 x)^3}-\frac{4719}{25 (3+5 x)^2}+\frac{14289}{25 (3+5 x)}\right ) \, dx\\ &=-\frac{1331}{250 (3+5 x)^2}+\frac{4719}{125 (3+5 x)}-\frac{343}{3} \log (2+3 x)+\frac{14289}{125} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0229934, size = 44, normalized size = 1.02 \[ \frac{11 \left (4290 x+2598 (5 x+3)^2 \log (-3 (5 x+3))+2453\right )}{250 (5 x+3)^2}-\frac{343}{3} \log (3 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 36, normalized size = 0.8 \begin{align*} -{\frac{1331}{250\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{4719}{375+625\,x}}-{\frac{343\,\ln \left ( 2+3\,x \right ) }{3}}+{\frac{14289\,\ln \left ( 3+5\,x \right ) }{125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02351, size = 49, normalized size = 1.14 \begin{align*} \frac{121 \,{\left (390 \, x + 223\right )}}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{14289}{125} \, \log \left (5 \, x + 3\right ) - \frac{343}{3} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.25902, size = 173, normalized size = 4.02 \begin{align*} \frac{85734 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 85750 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 141570 \, x + 80949}{750 \,{\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 = 0.149424, size = 34, normalized size = 0.79 \begin{align*} \frac{47190 x + 26983}{6250 x^{2} + 7500 x + 2250} + \frac{14289 \log{\left (x + \frac{3}{5} \right )}}{125} - \frac{343 \log{\left (x + \frac{2}{3} \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.09283, size = 45, normalized size = 1.05 \begin{align*} \frac{121 \,{\left (390 \, x + 223\right )}}{250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{14289}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{343}{3} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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