Optimal. Leaf size=32 \[ \frac {49}{44 (1-2 x)}+\frac {217}{484} \log (1-2 x)+\frac {1}{605} \log (5 x+3) \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {49}{44 (1-2 x)}+\frac {217}{484} \log (1-2 x)+\frac {1}{605} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac {49}{22 (-1+2 x)^2}+\frac {217}{242 (-1+2 x)}+\frac {1}{121 (3+5 x)}\right ) \, dx\\ &=\frac {49}{44 (1-2 x)}+\frac {217}{484} \log (1-2 x)+\frac {1}{605} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 40, normalized size = 1.25 \[ -\frac {245}{44 (2 (5 x+3)-11)}+\frac {1}{605} \log (5 x+3)+\frac {217}{484} \log (11-2 (5 x+3)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 37, normalized size = 1.16 \[ \frac {4 \, {\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 1085 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2695}{2420 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 43, normalized size = 1.34 \[ -\frac {49}{44 \, {\left (2 \, x - 1\right )}} - \frac {9}{20} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {1}{605} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.84 \[ \frac {217 \ln \left (2 x -1\right )}{484}+\frac {\ln \left (5 x +3\right )}{605}-\frac {49}{44 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 26, normalized size = 0.81 \[ -\frac {49}{44 \, {\left (2 \, x - 1\right )}} + \frac {1}{605} \, \log \left (5 \, x + 3\right ) + \frac {217}{484} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 22, normalized size = 0.69 \[ \frac {217\,\ln \left (x-\frac {1}{2}\right )}{484}+\frac {\ln \left (x+\frac {3}{5}\right )}{605}-\frac {49}{88\,\left (x-\frac {1}{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 24, normalized size = 0.75 \[ \frac {217 \log {\left (x - \frac {1}{2} \right )}}{484} + \frac {\log {\left (x + \frac {3}{5} \right )}}{605} - \frac {49}{88 x - 44} \]
Verification of antiderivative is not currently implemented for this CAS.
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