Optimal. Leaf size=64 \[ \frac {8}{5929 (1-2 x)}-\frac {27}{49 (3 x+2)}-\frac {125}{121 (5 x+3)}-\frac {1088 \log (1-2 x)}{456533}+\frac {1998}{343} \log (3 x+2)-\frac {7750 \log (5 x+3)}{1331} \]
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Rubi [A] time = 0.03, antiderivative size = 64, 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} \[ \frac {8}{5929 (1-2 x)}-\frac {27}{49 (3 x+2)}-\frac {125}{121 (5 x+3)}-\frac {1088 \log (1-2 x)}{456533}+\frac {1998}{343} \log (3 x+2)-\frac {7750 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac {16}{5929 (-1+2 x)^2}-\frac {2176}{456533 (-1+2 x)}+\frac {81}{49 (2+3 x)^2}+\frac {5994}{343 (2+3 x)}+\frac {625}{121 (3+5 x)^2}-\frac {38750}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {8}{5929 (1-2 x)}-\frac {27}{49 (2+3 x)}-\frac {125}{121 (3+5 x)}-\frac {1088 \log (1-2 x)}{456533}+\frac {1998}{343} \log (2+3 x)-\frac {7750 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A] time = 0.08, size = 59, normalized size = 0.92 \[ \frac {2 \left (-544 \log (1-2 x)+1329669 \log (6 x+4)+7 \left (\frac {44}{1-2 x}-\frac {35937}{6 x+4}-\frac {67375}{10 x+6}-189875 \log (10 x+6)\right )\right )}{456533} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 98, normalized size = 1.53 \[ -\frac {5354580 \, x^{2} + 2658250 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )} \log \left (5 \, x + 3\right ) - 2659338 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )} \log \left (3 \, x + 2\right ) + 1088 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )} \log \left (2 \, x - 1\right ) + 734888 \, x - 1694231}{456533 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 77, normalized size = 1.20 \[ -\frac {125}{121 \, {\left (5 \, x + 3\right )}} + \frac {5 \, {\left (\frac {1185937}{5 \, x + 3} - 215574\right )}}{65219 \, {\left (\frac {11}{5 \, x + 3} - 2\right )} {\left (\frac {1}{5 \, x + 3} + 3\right )}} + \frac {1998}{343} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {1088}{456533} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 53, normalized size = 0.83 \[ -\frac {1088 \ln \left (2 x -1\right )}{456533}+\frac {1998 \ln \left (3 x +2\right )}{343}-\frac {7750 \ln \left (5 x +3\right )}{1331}-\frac {125}{121 \left (5 x +3\right )}-\frac {27}{49 \left (3 x +2\right )}-\frac {8}{5929 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 54, normalized size = 0.84 \[ -\frac {69540 \, x^{2} + 9544 \, x - 22003}{5929 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )}} - \frac {7750}{1331} \, \log \left (5 \, x + 3\right ) + \frac {1998}{343} \, \log \left (3 \, x + 2\right ) - \frac {1088}{456533} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 47, normalized size = 0.73 \[ \frac {1998\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {1088\,\ln \left (x-\frac {1}{2}\right )}{456533}-\frac {7750\,\ln \left (x+\frac {3}{5}\right )}{1331}+\frac {\frac {2318\,x^2}{5929}+\frac {4772\,x}{88935}-\frac {22003}{177870}}{-x^3-\frac {23\,x^2}{30}+\frac {7\,x}{30}+\frac {1}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 54, normalized size = 0.84 \[ \frac {- 69540 x^{2} - 9544 x + 22003}{177870 x^{3} + 136367 x^{2} - 41503 x - 35574} - \frac {1088 \log {\left (x - \frac {1}{2} \right )}}{456533} - \frac {7750 \log {\left (x + \frac {3}{5} \right )}}{1331} + \frac {1998 \log {\left (x + \frac {2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
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