Optimal. Leaf size=64 \[ \frac {2}{847 (1-2 x)^2}+\frac {412}{65219 (1-2 x)}-\frac {125}{1331 (3+5 x)}-\frac {28296 \log (1-2 x)}{5021863}+\frac {81}{343} \log (2+3 x)-\frac {3375 \log (3+5 x)}{14641} \]
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Rubi [A]
time = 0.02, 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 = {90}
\begin {gather*} \frac {412}{65219 (1-2 x)}-\frac {125}{1331 (5 x+3)}+\frac {2}{847 (1-2 x)^2}-\frac {28296 \log (1-2 x)}{5021863}+\frac {81}{343} \log (3 x+2)-\frac {3375 \log (5 x+3)}{14641} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^3 (2+3 x) (3+5 x)^2} \, dx &=\int \left (-\frac {8}{847 (-1+2 x)^3}+\frac {824}{65219 (-1+2 x)^2}-\frac {56592}{5021863 (-1+2 x)}+\frac {243}{343 (2+3 x)}+\frac {625}{1331 (3+5 x)^2}-\frac {16875}{14641 (3+5 x)}\right ) \, dx\\ &=\frac {2}{847 (1-2 x)^2}+\frac {412}{65219 (1-2 x)}-\frac {125}{1331 (3+5 x)}-\frac {28296 \log (1-2 x)}{5021863}+\frac {81}{343} \log (2+3 x)-\frac {3375 \log (3+5 x)}{14641}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 60, normalized size = 0.94 \begin {gather*} \frac {3 \left (\frac {31724}{3-6 x}+\frac {11858}{3 (1-2 x)^2}-\frac {471625}{9+15 x}-9432 \log (3-6 x)+395307 \log (2+3 x)-385875 \log (-3 (3+5 x))\right )}{5021863} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 53, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {28620}{65219} x^{2}+\frac {24858}{65219} x -\frac {4427}{65219}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )}-\frac {28296 \ln \left (-1+2 x \right )}{5021863}+\frac {81 \ln \left (2+3 x \right )}{343}-\frac {3375 \ln \left (3+5 x \right )}{14641}\) | \(52\) |
default | \(\frac {2}{847 \left (-1+2 x \right )^{2}}-\frac {412}{65219 \left (-1+2 x \right )}-\frac {28296 \ln \left (-1+2 x \right )}{5021863}+\frac {81 \ln \left (2+3 x \right )}{343}-\frac {125}{1331 \left (3+5 x \right )}-\frac {3375 \ln \left (3+5 x \right )}{14641}\) | \(53\) |
norman | \(\frac {-\frac {121276}{195657} x^{2}+\frac {43585}{195657} x +\frac {88540}{195657} x^{3}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )}-\frac {28296 \ln \left (-1+2 x \right )}{5021863}+\frac {81 \ln \left (2+3 x \right )}{343}-\frac {3375 \ln \left (3+5 x \right )}{14641}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 54, normalized size = 0.84 \begin {gather*} -\frac {28620 \, x^{2} - 24858 \, x + 4427}{65219 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} - \frac {3375}{14641} \, \log \left (5 \, x + 3\right ) + \frac {81}{343} \, \log \left (3 \, x + 2\right ) - \frac {28296}{5021863} \, \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 = 1.28, size = 98, normalized size = 1.53 \begin {gather*} -\frac {2203740 \, x^{2} + 1157625 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1185921 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 28296 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 1914066 \, x + 340879}{5021863 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, 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 = 54, normalized size = 0.84 \begin {gather*} - \frac {28620 x^{2} - 24858 x + 4427}{1304380 x^{3} - 521752 x^{2} - 456533 x + 195657} - \frac {28296 \log {\left (x - \frac {1}{2} \right )}}{5021863} - \frac {3375 \log {\left (x + \frac {3}{5} \right )}}{14641} + \frac {81 \log {\left (x + \frac {2}{3} \right )}}{343} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.32, size = 66, normalized size = 1.03 \begin {gather*} -\frac {125}{1331 \, {\left (5 \, x + 3\right )}} + \frac {40 \, {\left (\frac {1518}{5 \, x + 3} - 241\right )}}{717409 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}^{2}} + \frac {81}{343} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {28296}{5021863} \, \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 = 47, normalized size = 0.73 \begin {gather*} \frac {81\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {28296\,\ln \left (x-\frac {1}{2}\right )}{5021863}-\frac {3375\,\ln \left (x+\frac {3}{5}\right )}{14641}+\frac {\frac {1431\,x^2}{65219}-\frac {12429\,x}{652190}+\frac {4427}{1304380}}{-x^3+\frac {2\,x^2}{5}+\frac {7\,x}{20}-\frac {3}{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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