Optimal. Leaf size=43 \[ \frac {1331}{196 (1-2 x)}+\frac {1}{441 (2+3 x)}+\frac {4719 \log (1-2 x)}{1372}+\frac {101 \log (2+3 x)}{3087} \]
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Rubi [A]
time = 0.01, antiderivative size = 43, 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 {1331}{196 (1-2 x)}+\frac {1}{441 (3 x+2)}+\frac {4719 \log (1-2 x)}{1372}+\frac {101 \log (3 x+2)}{3087} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^2} \, dx &=\int \left (\frac {1331}{98 (-1+2 x)^2}+\frac {4719}{686 (-1+2 x)}-\frac {1}{147 (2+3 x)^2}+\frac {101}{1029 (2+3 x)}\right ) \, dx\\ &=\frac {1331}{196 (1-2 x)}+\frac {1}{441 (2+3 x)}+\frac {4719 \log (1-2 x)}{1372}+\frac {101 \log (2+3 x)}{3087}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 40, normalized size = 0.93 \begin {gather*} \frac {-\frac {7 (23962+35929 x)}{-2+x+6 x^2}+42471 \log (5-10 x)+404 \log (5 (2+3 x))}{12348} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 36, normalized size = 0.84
method | result | size |
default | \(-\frac {1331}{196 \left (-1+2 x \right )}+\frac {4719 \ln \left (-1+2 x \right )}{1372}+\frac {1}{882+1323 x}+\frac {101 \ln \left (2+3 x \right )}{3087}\) | \(36\) |
risch | \(\frac {-\frac {35929 x}{1764}-\frac {11981}{882}}{\left (2+3 x \right ) \left (-1+2 x \right )}+\frac {4719 \ln \left (-1+2 x \right )}{1372}+\frac {101 \ln \left (2+3 x \right )}{3087}\) | \(39\) |
norman | \(\frac {\frac {35929 x^{2}}{294}-\frac {7985}{147}}{\left (2+3 x \right ) \left (-1+2 x \right )}+\frac {4719 \ln \left (-1+2 x \right )}{1372}+\frac {101 \ln \left (2+3 x \right )}{3087}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 34, normalized size = 0.79 \begin {gather*} -\frac {35929 \, x + 23962}{1764 \, {\left (6 \, x^{2} + x - 2\right )}} + \frac {101}{3087} \, \log \left (3 \, x + 2\right ) + \frac {4719}{1372} \, \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 = 0.46, size = 49, normalized size = 1.14 \begin {gather*} \frac {404 \, {\left (6 \, x^{2} + x - 2\right )} \log \left (3 \, x + 2\right ) + 42471 \, {\left (6 \, x^{2} + x - 2\right )} \log \left (2 \, x - 1\right ) - 251503 \, x - 167734}{12348 \, {\left (6 \, x^{2} + x - 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 36, normalized size = 0.84 \begin {gather*} \frac {- 35929 x - 23962}{10584 x^{2} + 1764 x - 3528} + \frac {4719 \log {\left (x - \frac {1}{2} \right )}}{1372} + \frac {101 \log {\left (x + \frac {2}{3} \right )}}{3087} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.02, size = 58, normalized size = 1.35 \begin {gather*} \frac {1}{441 \, {\left (3 \, x + 2\right )}} + \frac {3993}{686 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}} - \frac {125}{36} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) + \frac {4719}{1372} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 30, normalized size = 0.70 \begin {gather*} \frac {4719\,\ln \left (x-\frac {1}{2}\right )}{1372}+\frac {101\,\ln \left (x+\frac {2}{3}\right )}{3087}-\frac {\frac {35929\,x}{10584}+\frac {11981}{5292}}{x^2+\frac {x}{6}-\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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