Optimal. Leaf size=53 \[ \frac {4}{847 (1-2 x)}-\frac {25}{121 (3+5 x)}-\frac {412 \log (1-2 x)}{65219}+\frac {27}{49} \log (2+3 x)-\frac {725 \log (3+5 x)}{1331} \]
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Rubi [A]
time = 0.02, antiderivative size = 53, 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 {4}{847 (1-2 x)}-\frac {25}{121 (5 x+3)}-\frac {412 \log (1-2 x)}{65219}+\frac {27}{49} \log (3 x+2)-\frac {725 \log (5 x+3)}{1331} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^2 (2+3 x) (3+5 x)^2} \, dx &=\int \left (\frac {8}{847 (-1+2 x)^2}-\frac {824}{65219 (-1+2 x)}+\frac {81}{49 (2+3 x)}+\frac {125}{121 (3+5 x)^2}-\frac {3625}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {4}{847 (1-2 x)}-\frac {25}{121 (3+5 x)}-\frac {412 \log (1-2 x)}{65219}+\frac {27}{49} \log (2+3 x)-\frac {725 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 48, normalized size = 0.91 \begin {gather*} \frac {-\frac {77 (-163+370 x)}{-3+x+10 x^2}-412 \log (3-6 x)+35937 \log (2+3 x)-35525 \log (-3 (3+5 x))}{65219} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 44, normalized size = 0.83
method | result | size |
default | \(-\frac {4}{847 \left (-1+2 x \right )}-\frac {412 \ln \left (-1+2 x \right )}{65219}+\frac {27 \ln \left (2+3 x \right )}{49}-\frac {25}{121 \left (3+5 x \right )}-\frac {725 \ln \left (3+5 x \right )}{1331}\) | \(44\) |
risch | \(\frac {-\frac {370 x}{847}+\frac {163}{847}}{\left (3+5 x \right ) \left (-1+2 x \right )}-\frac {412 \ln \left (-1+2 x \right )}{65219}+\frac {27 \ln \left (2+3 x \right )}{49}-\frac {725 \ln \left (3+5 x \right )}{1331}\) | \(47\) |
norman | \(\frac {\frac {3700 x^{2}}{847}-\frac {947}{847}}{\left (3+5 x \right ) \left (-1+2 x \right )}-\frac {412 \ln \left (-1+2 x \right )}{65219}+\frac {27 \ln \left (2+3 x \right )}{49}-\frac {725 \ln \left (3+5 x \right )}{1331}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 42, normalized size = 0.79 \begin {gather*} -\frac {370 \, x - 163}{847 \, {\left (10 \, x^{2} + x - 3\right )}} - \frac {725}{1331} \, \log \left (5 \, x + 3\right ) + \frac {27}{49} \, \log \left (3 \, x + 2\right ) - \frac {412}{65219} \, \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 = 0.51, size = 65, normalized size = 1.23 \begin {gather*} -\frac {35525 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) - 35937 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (3 \, x + 2\right ) + 412 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) + 28490 \, x - 12551}{65219 \, {\left (10 \, x^{2} + x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 44, normalized size = 0.83 \begin {gather*} \frac {163 - 370 x}{8470 x^{2} + 847 x - 2541} - \frac {412 \log {\left (x - \frac {1}{2} \right )}}{65219} - \frac {725 \log {\left (x + \frac {3}{5} \right )}}{1331} + \frac {27 \log {\left (x + \frac {2}{3} \right )}}{49} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.52, size = 55, normalized size = 1.04 \begin {gather*} -\frac {25}{121 \, {\left (5 \, x + 3\right )}} + \frac {40}{9317 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} + \frac {27}{49} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {412}{65219} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 36, normalized size = 0.68 \begin {gather*} \frac {27\,\ln \left (x+\frac {2}{3}\right )}{49}-\frac {412\,\ln \left (x-\frac {1}{2}\right )}{65219}-\frac {725\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {\frac {37\,x}{847}-\frac {163}{8470}}{x^2+\frac {x}{10}-\frac {3}{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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