Optimal. Leaf size=75 \[ \frac {4}{3773 (1-2 x)^2}+\frac {1072}{290521 (1-2 x)}+\frac {27}{686 (2+3 x)^2}+\frac {1107}{2401 (2+3 x)}-\frac {89792 \log (1-2 x)}{22370117}-\frac {39393 \log (2+3 x)}{16807}+\frac {3125 \log (3+5 x)}{1331} \]
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Rubi [A]
time = 0.03, antiderivative size = 75, 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 {1072}{290521 (1-2 x)}+\frac {1107}{2401 (3 x+2)}+\frac {4}{3773 (1-2 x)^2}+\frac {27}{686 (3 x+2)^2}-\frac {89792 \log (1-2 x)}{22370117}-\frac {39393 \log (3 x+2)}{16807}+\frac {3125 \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)^3 (2+3 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {16}{3773 (-1+2 x)^3}+\frac {2144}{290521 (-1+2 x)^2}-\frac {179584}{22370117 (-1+2 x)}-\frac {81}{343 (2+3 x)^3}-\frac {3321}{2401 (2+3 x)^2}-\frac {118179}{16807 (2+3 x)}+\frac {15625}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {4}{3773 (1-2 x)^2}+\frac {1072}{290521 (1-2 x)}+\frac {27}{686 (2+3 x)^2}+\frac {1107}{2401 (2+3 x)}-\frac {89792 \log (1-2 x)}{22370117}-\frac {39393 \log (2+3 x)}{16807}+\frac {3125 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 58, normalized size = 0.77 \begin {gather*} \frac {\frac {77 \left (569697-1414978 x-1006716 x^2+3176136 x^3\right )}{\left (-2+x+6 x^2\right )^2}-179584 \log (5-10 x)-104864166 \log (5 (2+3 x))+105043750 \log (3+5 x)}{44740234} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 62, normalized size = 0.83
method | result | size |
risch | \(\frac {\frac {1588068}{290521} x^{3}-\frac {503358}{290521} x^{2}-\frac {707489}{290521} x +\frac {569697}{581042}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{2}}-\frac {89792 \ln \left (-1+2 x \right )}{22370117}-\frac {39393 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{1331}\) | \(57\) |
norman | \(\frac {-\frac {6367401}{290521} x^{4}-\frac {534399}{290521} x^{3}+\frac {14258815}{1162084} x^{2}-\frac {845281}{581042}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{2}}-\frac {89792 \ln \left (-1+2 x \right )}{22370117}-\frac {39393 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{1331}\) | \(58\) |
default | \(\frac {4}{3773 \left (-1+2 x \right )^{2}}-\frac {1072}{290521 \left (-1+2 x \right )}-\frac {89792 \ln \left (-1+2 x \right )}{22370117}+\frac {27}{686 \left (2+3 x \right )^{2}}+\frac {1107}{2401 \left (2+3 x \right )}-\frac {39393 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{1331}\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.46, size = 64, normalized size = 0.85 \begin {gather*} \frac {3176136 \, x^{3} - 1006716 \, x^{2} - 1414978 \, x + 569697}{581042 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} + \frac {3125}{1331} \, \log \left (5 \, x + 3\right ) - \frac {39393}{16807} \, \log \left (3 \, x + 2\right ) - \frac {89792}{22370117} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 123 vs.
\(2 (61) = 122\).
time = 0.69, size = 123, normalized size = 1.64 \begin {gather*} \frac {244562472 \, x^{3} - 77517132 \, x^{2} + 105043750 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 104864166 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 179584 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (2 \, x - 1\right ) - 108953306 \, x + 43866669}{44740234 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 65, normalized size = 0.87 \begin {gather*} - \frac {- 3176136 x^{3} + 1006716 x^{2} + 1414978 x - 569697}{20917512 x^{4} + 6972504 x^{3} - 13363966 x^{2} - 2324168 x + 2324168} - \frac {89792 \log {\left (x - \frac {1}{2} \right )}}{22370117} + \frac {3125 \log {\left (x + \frac {3}{5} \right )}}{1331} - \frac {39393 \log {\left (x + \frac {2}{3} \right )}}{16807} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.52, size = 59, normalized size = 0.79 \begin {gather*} \frac {3176136 \, x^{3} - 1006716 \, x^{2} - 1414978 \, x + 569697}{581042 \, {\left (3 \, x + 2\right )}^{2} {\left (2 \, x - 1\right )}^{2}} + \frac {3125}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {39393}{16807} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {89792}{22370117} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 56, normalized size = 0.75 \begin {gather*} \frac {3125\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {39393\,\ln \left (x+\frac {2}{3}\right )}{16807}-\frac {89792\,\ln \left (x-\frac {1}{2}\right )}{22370117}-\frac {-\frac {44113\,x^3}{290521}+\frac {83893\,x^2}{1743126}+\frac {707489\,x}{10458756}-\frac {189899}{6972504}}{x^4+\frac {x^3}{3}-\frac {23\,x^2}{36}-\frac {x}{9}+\frac {1}{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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