Optimal. Leaf size=32 \[ \frac {49}{44 (1-2 x)}+\frac {217}{484} \log (1-2 x)+\frac {1}{605} \log (3+5 x) \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {49}{44 (1-2 x)}+\frac {217}{484} \log (1-2 x)+\frac {1}{605} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
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 = 0.01, size = 40, normalized size = 1.25 \begin {gather*} -\frac {245}{44 (-11+2 (3+5 x))}+\frac {1}{605} \log (3+5 x)+\frac {217}{484} \log (11-2 (3+5 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 27, normalized size = 0.84
method | result | size |
risch | \(-\frac {49}{88 \left (-\frac {1}{2}+x \right )}+\frac {217 \ln \left (-1+2 x \right )}{484}+\frac {\ln \left (3+5 x \right )}{605}\) | \(25\) |
default | \(-\frac {49}{44 \left (-1+2 x \right )}+\frac {217 \ln \left (-1+2 x \right )}{484}+\frac {\ln \left (3+5 x \right )}{605}\) | \(27\) |
norman | \(-\frac {49 x}{22 \left (-1+2 x \right )}+\frac {217 \ln \left (-1+2 x \right )}{484}+\frac {\ln \left (3+5 x \right )}{605}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.38, size = 26, normalized size = 0.81 \begin {gather*} -\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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 37, normalized size = 1.16 \begin {gather*} \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 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 24, normalized size = 0.75 \begin {gather*} \frac {217 \log {\left (x - \frac {1}{2} \right )}}{484} + \frac {\log {\left (x + \frac {3}{5} \right )}}{605} - \frac {49}{88 x - 44} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.68, size = 43, normalized size = 1.34 \begin {gather*} -\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 ) \end {gather*}
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 \begin {gather*} \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 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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