Optimal. Leaf size=53 \[ -\frac {9}{7 (2+3 x)}-\frac {25}{11 (3+5 x)}-\frac {8 \log (1-2 x)}{5929}+\frac {648}{49} \log (2+3 x)-\frac {1600}{121} \log (3+5 x) \]
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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 {9}{7 (3 x+2)}-\frac {25}{11 (5 x+3)}-\frac {8 \log (1-2 x)}{5929}+\frac {648}{49} \log (3 x+2)-\frac {1600}{121} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)^2} \, dx &=\int \left (-\frac {16}{5929 (-1+2 x)}+\frac {27}{7 (2+3 x)^2}+\frac {1944}{49 (2+3 x)}+\frac {125}{11 (3+5 x)^2}-\frac {8000}{121 (3+5 x)}\right ) \, dx\\ &=-\frac {9}{7 (2+3 x)}-\frac {25}{11 (3+5 x)}-\frac {8 \log (1-2 x)}{5929}+\frac {648}{49} \log (2+3 x)-\frac {1600}{121} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 47, normalized size = 0.89 \begin {gather*} \frac {2 \left (-\frac {7623}{4+6 x}-\frac {13475}{6+10 x}-4 \log (1-2 x)+39204 \log (4+6 x)-39200 \log (6+10 x)\right )}{5929} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 44, normalized size = 0.83
method | result | size |
default | \(-\frac {8 \ln \left (-1+2 x \right )}{5929}-\frac {9}{7 \left (2+3 x \right )}+\frac {648 \ln \left (2+3 x \right )}{49}-\frac {25}{11 \left (3+5 x \right )}-\frac {1600 \ln \left (3+5 x \right )}{121}\) | \(44\) |
risch | \(\frac {-\frac {1020 x}{77}-\frac {647}{77}}{\left (2+3 x \right ) \left (3+5 x \right )}-\frac {8 \ln \left (-1+2 x \right )}{5929}+\frac {648 \ln \left (2+3 x \right )}{49}-\frac {1600 \ln \left (3+5 x \right )}{121}\) | \(47\) |
norman | \(\frac {\frac {3235}{154} x^{2}+\frac {6173}{462} x}{\left (2+3 x \right ) \left (3+5 x \right )}-\frac {8 \ln \left (-1+2 x \right )}{5929}+\frac {648 \ln \left (2+3 x \right )}{49}-\frac {1600 \ln \left (3+5 x \right )}{121}\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 44, normalized size = 0.83 \begin {gather*} -\frac {1020 \, x + 647}{77 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}} - \frac {1600}{121} \, \log \left (5 \, x + 3\right ) + \frac {648}{49} \, \log \left (3 \, x + 2\right ) - \frac {8}{5929} \, \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 = 1.31, size = 73, normalized size = 1.38 \begin {gather*} -\frac {78400 \, {\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 78408 \, {\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 8 \, {\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (2 \, x - 1\right ) + 78540 \, x + 49819}{5929 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 44, normalized size = 0.83 \begin {gather*} - \frac {1020 x + 647}{1155 x^{2} + 1463 x + 462} - \frac {8 \log {\left (x - \frac {1}{2} \right )}}{5929} - \frac {1600 \log {\left (x + \frac {3}{5} \right )}}{121} + \frac {648 \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 = 1.16, size = 53, normalized size = 1.00 \begin {gather*} -\frac {25}{11 \, {\left (5 \, x + 3\right )}} + \frac {135}{7 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}} + \frac {648}{49} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {8}{5929} \, \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 {648\,\ln \left (x+\frac {2}{3}\right )}{49}-\frac {8\,\ln \left (x-\frac {1}{2}\right )}{5929}-\frac {1600\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {\frac {68\,x}{77}+\frac {647}{1155}}{x^2+\frac {19\,x}{15}+\frac {2}{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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