Optimal. Leaf size=32 \[ \frac {1}{11 (1-2 x)}-\frac {5}{121} \log (1-2 x)+\frac {5}{121} \log (3+5 x) \]
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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 = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {46}
\begin {gather*} \frac {1}{11 (1-2 x)}-\frac {5}{121} \log (1-2 x)+\frac {5}{121} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 46
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac {2}{11 (-1+2 x)^2}-\frac {10}{121 (-1+2 x)}+\frac {25}{121 (3+5 x)}\right ) \, dx\\ &=\frac {1}{11 (1-2 x)}-\frac {5}{121} \log (1-2 x)+\frac {5}{121} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 38, normalized size = 1.19 \begin {gather*} \frac {-11+(5-10 x) \log (1-2 x)+5 (-1+2 x) \log (6+10 x)}{121 (-1+2 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 27, normalized size = 0.84
method | result | size |
risch | \(-\frac {1}{22 \left (-\frac {1}{2}+x \right )}-\frac {5 \ln \left (-1+2 x \right )}{121}+\frac {5 \ln \left (3+5 x \right )}{121}\) | \(25\) |
default | \(-\frac {1}{11 \left (-1+2 x \right )}-\frac {5 \ln \left (-1+2 x \right )}{121}+\frac {5 \ln \left (3+5 x \right )}{121}\) | \(27\) |
norman | \(-\frac {2 x}{11 \left (-1+2 x \right )}-\frac {5 \ln \left (-1+2 x \right )}{121}+\frac {5 \ln \left (3+5 x \right )}{121}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 26, normalized size = 0.81 \begin {gather*} -\frac {1}{11 \, {\left (2 \, x - 1\right )}} + \frac {5}{121} \, \log \left (5 \, x + 3\right ) - \frac {5}{121} \, \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 = 0.38, size = 37, normalized size = 1.16 \begin {gather*} \frac {5 \, {\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) - 5 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 11}{121 \, {\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 = 26, normalized size = 0.81 \begin {gather*} - \frac {5 \log {\left (x - \frac {1}{2} \right )}}{121} + \frac {5 \log {\left (x + \frac {3}{5} \right )}}{121} - \frac {1}{22 x - 11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.52, size = 25, normalized size = 0.78 \begin {gather*} -\frac {1}{11 \, {\left (2 \, x - 1\right )}} + \frac {5}{121} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 26, normalized size = 0.81 \begin {gather*} -\frac {5\,\ln \left (\frac {2\,x-1}{5\,x+3}\right )}{121}-\frac {1}{11\,\left (2\,x-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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