Optimal. Leaf size=32 \[ -\frac {1}{63 (3 x+2)}-\frac {121}{98} \log (1-2 x)-\frac {68}{441} \log (3 x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 32, 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} \[ -\frac {1}{63 (3 x+2)}-\frac {121}{98} \log (1-2 x)-\frac {68}{441} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x) (2+3 x)^2} \, dx &=\int \left (-\frac {121}{49 (-1+2 x)}+\frac {1}{21 (2+3 x)^2}-\frac {68}{147 (2+3 x)}\right ) \, dx\\ &=-\frac {1}{63 (2+3 x)}-\frac {121}{98} \log (1-2 x)-\frac {68}{441} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 30, normalized size = 0.94 \[ \frac {1}{882} \left (-\frac {14}{3 x+2}-1089 \log (1-2 x)-136 \log (6 x+4)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 37, normalized size = 1.16 \[ -\frac {136 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 1089 \, {\left (3 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 14}{882 \, {\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.09, size = 43, normalized size = 1.34 \[ -\frac {1}{63 \, {\left (3 \, x + 2\right )}} + \frac {25}{18} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) - \frac {121}{98} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.84 \[ -\frac {121 \ln \left (2 x -1\right )}{98}-\frac {68 \ln \left (3 x +2\right )}{441}-\frac {1}{63 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 26, normalized size = 0.81 \[ -\frac {1}{63 \, {\left (3 \, x + 2\right )}} - \frac {68}{441} \, \log \left (3 \, x + 2\right ) - \frac {121}{98} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 22, normalized size = 0.69 \[ -\frac {121\,\ln \left (x-\frac {1}{2}\right )}{98}-\frac {68\,\ln \left (x+\frac {2}{3}\right )}{441}-\frac {1}{189\,\left (x+\frac {2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 27, normalized size = 0.84 \[ - \frac {121 \log {\left (x - \frac {1}{2} \right )}}{98} - \frac {68 \log {\left (x + \frac {2}{3} \right )}}{441} - \frac {1}{189 x + 126} \]
Verification of antiderivative is not currently implemented for this CAS.
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