Optimal. Leaf size=32 \[ \frac {11}{14 (1-2 x)}+\frac {1}{49} \log (1-2 x)-\frac {1}{49} \log (2+3 x) \]
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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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} \frac {11}{14 (1-2 x)}+\frac {1}{49} \log (1-2 x)-\frac {1}{49} \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 (2+3 x)} \, dx &=\int \left (\frac {11}{7 (-1+2 x)^2}+\frac {2}{49 (-1+2 x)}-\frac {3}{49 (2+3 x)}\right ) \, dx\\ &=\frac {11}{14 (1-2 x)}+\frac {1}{49} \log (1-2 x)-\frac {1}{49} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 37, normalized size = 1.16 \begin {gather*} \frac {-77+(-2+4 x) \log (1-2 x)+(2-4 x) \log (4+6 x)}{98 (-1+2 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 27, normalized size = 0.84
method | result | size |
risch | \(-\frac {11}{28 \left (-\frac {1}{2}+x \right )}+\frac {\ln \left (-1+2 x \right )}{49}-\frac {\ln \left (2+3 x \right )}{49}\) | \(25\) |
default | \(-\frac {11}{14 \left (-1+2 x \right )}+\frac {\ln \left (-1+2 x \right )}{49}-\frac {\ln \left (2+3 x \right )}{49}\) | \(27\) |
norman | \(-\frac {11 x}{7 \left (-1+2 x \right )}+\frac {\ln \left (-1+2 x \right )}{49}-\frac {\ln \left (2+3 x \right )}{49}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 26, normalized size = 0.81 \begin {gather*} -\frac {11}{14 \, {\left (2 \, x - 1\right )}} - \frac {1}{49} \, \log \left (3 \, x + 2\right ) + \frac {1}{49} \, \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 = 0.78, size = 37, normalized size = 1.16 \begin {gather*} -\frac {2 \, {\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) - 2 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) + 77}{98 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 22, normalized size = 0.69 \begin {gather*} \frac {\log {\left (x - \frac {1}{2} \right )}}{49} - \frac {\log {\left (x + \frac {2}{3} \right )}}{49} - \frac {11}{28 x - 14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.76, size = 25, normalized size = 0.78 \begin {gather*} -\frac {11}{14 \, {\left (2 \, x - 1\right )}} - \frac {1}{49} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 18, normalized size = 0.56 \begin {gather*} -\frac {2\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{49}-\frac {11}{28\,\left (x-\frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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