Optimal. Leaf size=21 \[ -\frac {11}{14} \log (1-2 x)-\frac {1}{21} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} -\frac {11}{14} \log (1-2 x)-\frac {1}{21} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x) (2+3 x)} \, dx &=\int \left (-\frac {11}{7 (-1+2 x)}-\frac {1}{7 (2+3 x)}\right ) \, dx\\ &=-\frac {11}{14} \log (1-2 x)-\frac {1}{21} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} -\frac {11}{14} \log (1-2 x)-\frac {1}{21} \log (2+3 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 18, normalized size = 0.86
method | result | size |
default | \(-\frac {11 \ln \left (-1+2 x \right )}{14}-\frac {\ln \left (2+3 x \right )}{21}\) | \(18\) |
norman | \(-\frac {11 \ln \left (-1+2 x \right )}{14}-\frac {\ln \left (2+3 x \right )}{21}\) | \(18\) |
risch | \(-\frac {11 \ln \left (-1+2 x \right )}{14}-\frac {\ln \left (2+3 x \right )}{21}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 17, normalized size = 0.81 \begin {gather*} -\frac {1}{21} \, \log \left (3 \, x + 2\right ) - \frac {11}{14} \, \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 = 0.45, size = 17, normalized size = 0.81 \begin {gather*} -\frac {1}{21} \, \log \left (3 \, x + 2\right ) - \frac {11}{14} \, \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 = 19, normalized size = 0.90 \begin {gather*} - \frac {11 \log {\left (x - \frac {1}{2} \right )}}{14} - \frac {\log {\left (x + \frac {2}{3} \right )}}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.70, size = 19, normalized size = 0.90 \begin {gather*} -\frac {1}{21} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {11}{14} \, \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 = 0.07, size = 13, normalized size = 0.62 \begin {gather*} -\frac {11\,\ln \left (x-\frac {1}{2}\right )}{14}-\frac {\ln \left (x+\frac {2}{3}\right )}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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