Optimal. Leaf size=50 \[ \frac{343}{3 (3 x+2)}+\frac{8712}{25 (5 x+3)}-\frac{1331}{50 (5 x+3)^2}-1617 \log (3 x+2)+1617 \log (5 x+3) \]
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Rubi [A] time = 0.0228256, antiderivative size = 50, 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} \[ \frac{343}{3 (3 x+2)}+\frac{8712}{25 (5 x+3)}-\frac{1331}{50 (5 x+3)^2}-1617 \log (3 x+2)+1617 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx &=\int \left (-\frac{343}{(2+3 x)^2}-\frac{4851}{2+3 x}+\frac{1331}{5 (3+5 x)^3}-\frac{8712}{5 (3+5 x)^2}+\frac{8085}{3+5 x}\right ) \, dx\\ &=\frac{343}{3 (2+3 x)}-\frac{1331}{50 (3+5 x)^2}+\frac{8712}{25 (3+5 x)}-1617 \log (2+3 x)+1617 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0256996, size = 48, normalized size = 0.96 \[ \frac{343}{9 x+6}+\frac{8712}{125 x+75}-\frac{1331}{50 (5 x+3)^2}-1617 \log (5 (3 x+2))+1617 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 45, normalized size = 0.9 \begin{align*}{\frac{343}{6+9\,x}}-{\frac{1331}{50\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{8712}{75+125\,x}}-1617\,\ln \left ( 2+3\,x \right ) +1617\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.99799, size = 62, normalized size = 1.24 \begin{align*} \frac{1212830 \, x^{2} + 1495689 \, x + 459996}{150 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + 1617 \, \log \left (5 \, x + 3\right ) - 1617 \, \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 = 1.37018, size = 242, normalized size = 4.84 \begin{align*} \frac{1212830 \, x^{2} + 242550 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 242550 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) + 1495689 \, x + 459996}{150 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.150972, size = 41, normalized size = 0.82 \begin{align*} \frac{1212830 x^{2} + 1495689 x + 459996}{11250 x^{3} + 21000 x^{2} + 13050 x + 2700} + 1617 \log{\left (x + \frac{3}{5} \right )} - 1617 \log{\left (x + \frac{2}{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.66612, size = 66, normalized size = 1.32 \begin{align*} \frac{343}{3 \,{\left (3 \, x + 2\right )}} - \frac{1089 \,{\left (\frac{14}{3 \, x + 2} - 59\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + 1617 \, \log \left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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