Optimal. Leaf size=26 \[ -\frac {25 x}{6}-\frac {121}{28} \log (1-2 x)+\frac {1}{63} \log (3 x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 26, 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 = {72} \[ -\frac {25 x}{6}-\frac {121}{28} \log (1-2 x)+\frac {1}{63} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x) (2+3 x)} \, dx &=\int \left (-\frac {25}{6}-\frac {121}{14 (-1+2 x)}+\frac {1}{21 (2+3 x)}\right ) \, dx\\ &=-\frac {25 x}{6}-\frac {121}{28} \log (1-2 x)+\frac {1}{63} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 32, normalized size = 1.23 \[ -\frac {5}{6} (5 x+3)-\frac {121}{28} \log (5-10 x)+\frac {1}{63} \log (5 (3 x+2)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 20, normalized size = 0.77 \[ -\frac {25}{6} \, x + \frac {1}{63} \, \log \left (3 \, x + 2\right ) - \frac {121}{28} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 22, normalized size = 0.85 \[ -\frac {25}{6} \, x + \frac {1}{63} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {121}{28} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 21, normalized size = 0.81 \[ -\frac {25 x}{6}-\frac {121 \ln \left (2 x -1\right )}{28}+\frac {\ln \left (3 x +2\right )}{63} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 20, normalized size = 0.77 \[ -\frac {25}{6} \, x + \frac {1}{63} \, \log \left (3 \, x + 2\right ) - \frac {121}{28} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 16, normalized size = 0.62 \[ \frac {\ln \left (x+\frac {2}{3}\right )}{63}-\frac {121\,\ln \left (x-\frac {1}{2}\right )}{28}-\frac {25\,x}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 22, normalized size = 0.85 \[ - \frac {25 x}{6} - \frac {121 \log {\left (x - \frac {1}{2} \right )}}{28} + \frac {\log {\left (x + \frac {2}{3} \right )}}{63} \]
Verification of antiderivative is not currently implemented for this CAS.
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