Optimal. Leaf size=37 \[ -\frac {125 x}{18}+\frac {1}{189 (3 x+2)}-\frac {1331}{196} \log (1-2 x)+\frac {103 \log (3 x+2)}{1323} \]
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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} \[ -\frac {125 x}{18}+\frac {1}{189 (3 x+2)}-\frac {1331}{196} \log (1-2 x)+\frac {103 \log (3 x+2)}{1323} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^2} \, dx &=\int \left (-\frac {125}{18}-\frac {1331}{98 (-1+2 x)}-\frac {1}{63 (2+3 x)^2}+\frac {103}{441 (2+3 x)}\right ) \, dx\\ &=-\frac {125 x}{18}+\frac {1}{189 (2+3 x)}-\frac {1331}{196} \log (1-2 x)+\frac {103 \log (2+3 x)}{1323}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 37, normalized size = 1.00 \[ \frac {18375 (1-2 x)+\frac {28}{3 x+2}-35937 \log (1-2 x)+412 \log (6 x+4)}{5292} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 45, normalized size = 1.22 \[ -\frac {110250 \, x^{2} - 412 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 35937 \, {\left (3 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 73500 \, x - 28}{5292 \, {\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 47, normalized size = 1.27 \[ -\frac {125}{18} \, x + \frac {1}{189 \, {\left (3 \, x + 2\right )}} + \frac {725}{108} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) - \frac {1331}{196} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) - \frac {125}{27} \]
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 \[ -\frac {125 x}{18}-\frac {1331 \ln \left (2 x -1\right )}{196}+\frac {103 \ln \left (3 x +2\right )}{1323}+\frac {1}{567 x +378} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 29, normalized size = 0.78 \[ -\frac {125}{18} \, x + \frac {1}{189 \, {\left (3 \, x + 2\right )}} + \frac {103}{1323} \, \log \left (3 \, x + 2\right ) - \frac {1331}{196} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 23, normalized size = 0.62 \[ \frac {103\,\ln \left (x+\frac {2}{3}\right )}{1323}-\frac {1331\,\ln \left (x-\frac {1}{2}\right )}{196}-\frac {125\,x}{18}+\frac {1}{567\,\left (x+\frac {2}{3}\right )} \]
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 \[ - \frac {125 x}{18} - \frac {1331 \log {\left (x - \frac {1}{2} \right )}}{196} + \frac {103 \log {\left (x + \frac {2}{3} \right )}}{1323} + \frac {1}{567 x + 378} \]
Verification of antiderivative is not currently implemented for this CAS.
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