Optimal. Leaf size=37 \[ -\frac {8 x}{75}-\frac {1331}{125 (5 x+3)}+\frac {343}{9} \log (3 x+2)-\frac {4719}{125} \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 37, normalized size of antiderivative = 1.00, 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} \[ -\frac {8 x}{75}-\frac {1331}{125 (5 x+3)}+\frac {343}{9} \log (3 x+2)-\frac {4719}{125} \log (5 x+3) \]
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)^2} \, dx &=\int \left (-\frac {8}{75}+\frac {343}{3 (2+3 x)}+\frac {1331}{25 (3+5 x)^2}-\frac {4719}{25 (3+5 x)}\right ) \, dx\\ &=-\frac {8 x}{75}-\frac {1331}{125 (3+5 x)}+\frac {343}{9} \log (2+3 x)-\frac {4719}{125} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 36, normalized size = 0.97 \[ \frac {-120 x-\frac {11979}{5 x+3}+42875 \log (3 x+2)-42471 \log (-3 (5 x+3))-80}{1125} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 45, normalized size = 1.22 \[ -\frac {600 \, x^{2} + 42471 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 42875 \, {\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 360 \, x + 11979}{1125 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.07, size = 47, normalized size = 1.27 \[ -\frac {8}{75} \, x - \frac {1331}{125 \, {\left (5 \, x + 3\right )}} - \frac {404}{1125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {343}{9} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {8}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 30, normalized size = 0.81 \[ -\frac {8 x}{75}+\frac {343 \ln \left (3 x +2\right )}{9}-\frac {4719 \ln \left (5 x +3\right )}{125}-\frac {1331}{125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 29, normalized size = 0.78 \[ -\frac {8}{75} \, x - \frac {1331}{125 \, {\left (5 \, x + 3\right )}} - \frac {4719}{125} \, \log \left (5 \, x + 3\right ) + \frac {343}{9} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 25, normalized size = 0.68 \[ \frac {343\,\ln \left (x+\frac {2}{3}\right )}{9}-\frac {8\,x}{75}-\frac {4719\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {1331}{625\,\left (x+\frac {3}{5}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 31, normalized size = 0.84 \[ - \frac {8 x}{75} - \frac {4719 \log {\left (x + \frac {3}{5} \right )}}{125} + \frac {343 \log {\left (x + \frac {2}{3} \right )}}{9} - \frac {1331}{625 x + 375} \]
Verification of antiderivative is not currently implemented for this CAS.
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