Optimal. Leaf size=26 \[ -\frac {25 x}{6}-\frac {121}{28} \log (1-2 x)+\frac {1}{63} \log (2+3 x) \]
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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 = {84}
\begin {gather*} -\frac {25 x}{6}-\frac {121}{28} \log (1-2 x)+\frac {1}{63} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 84
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 \begin {gather*} -\frac {5}{6} (3+5 x)-\frac {121}{28} \log (5-10 x)+\frac {1}{63} \log (5 (2+3 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 21, normalized size = 0.81
method | result | size |
default | \(-\frac {25 x}{6}-\frac {121 \ln \left (-1+2 x \right )}{28}+\frac {\ln \left (2+3 x \right )}{63}\) | \(21\) |
norman | \(-\frac {25 x}{6}-\frac {121 \ln \left (-1+2 x \right )}{28}+\frac {\ln \left (2+3 x \right )}{63}\) | \(21\) |
risch | \(-\frac {25 x}{6}-\frac {121 \ln \left (-1+2 x \right )}{28}+\frac {\ln \left (2+3 x \right )}{63}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 20, normalized size = 0.77 \begin {gather*} -\frac {25}{6} \, x + \frac {1}{63} \, \log \left (3 \, x + 2\right ) - \frac {121}{28} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 20, normalized size = 0.77 \begin {gather*} -\frac {25}{6} \, x + \frac {1}{63} \, \log \left (3 \, x + 2\right ) - \frac {121}{28} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 22, normalized size = 0.85 \begin {gather*} - \frac {25 x}{6} - \frac {121 \log {\left (x - \frac {1}{2} \right )}}{28} + \frac {\log {\left (x + \frac {2}{3} \right )}}{63} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.69, size = 22, normalized size = 0.85 \begin {gather*} -\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 ) \end {gather*}
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 \begin {gather*} \frac {\ln \left (x+\frac {2}{3}\right )}{63}-\frac {121\,\ln \left (x-\frac {1}{2}\right )}{28}-\frac {25\,x}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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