Optimal. Leaf size=97 \[ \frac {27}{28 (2+3 x)^4}+\frac {963}{49 (2+3 x)^3}+\frac {102114}{343 (2+3 x)^2}+\frac {11984706}{2401 (2+3 x)}-\frac {3125}{22 (3+5 x)^2}+\frac {509375}{121 (3+5 x)}-\frac {128 \log (1-2 x)}{22370117}-\frac {631722537 \log (2+3 x)}{16807}+\frac {50028125 \log (3+5 x)}{1331} \]
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Rubi [A]
time = 0.03, antiderivative size = 97, 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 {11984706}{2401 (3 x+2)}+\frac {509375}{121 (5 x+3)}+\frac {102114}{343 (3 x+2)^2}-\frac {3125}{22 (5 x+3)^2}+\frac {963}{49 (3 x+2)^3}+\frac {27}{28 (3 x+2)^4}-\frac {128 \log (1-2 x)}{22370117}-\frac {631722537 \log (3 x+2)}{16807}+\frac {50028125 \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+3 x)^5 (3+5 x)^3} \, dx &=\int \left (-\frac {256}{22370117 (-1+2 x)}-\frac {81}{7 (2+3 x)^5}-\frac {8667}{49 (2+3 x)^4}-\frac {612684}{343 (2+3 x)^3}-\frac {35954118}{2401 (2+3 x)^2}-\frac {1895167611}{16807 (2+3 x)}+\frac {15625}{11 (3+5 x)^3}-\frac {2546875}{121 (3+5 x)^2}+\frac {250140625}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {27}{28 (2+3 x)^4}+\frac {963}{49 (2+3 x)^3}+\frac {102114}{343 (2+3 x)^2}+\frac {11984706}{2401 (2+3 x)}-\frac {3125}{22 (3+5 x)^2}+\frac {509375}{121 (3+5 x)}-\frac {128 \log (1-2 x)}{22370117}-\frac {631722537 \log (2+3 x)}{16807}+\frac {50028125 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A]
time = 0.04, size = 95, normalized size = 0.98 \begin {gather*} \frac {27}{28 (2+3 x)^4}+\frac {963}{49 (2+3 x)^3}+\frac {102114}{343 (2+3 x)^2}+\frac {11984706}{2401 (2+3 x)}-\frac {3125}{22 (3+5 x)^2}+\frac {509375}{363+605 x}-\frac {128 \log (1-2 x)}{22370117}-\frac {631722537 \log (4+6 x)}{16807}+\frac {50028125 \log (6+10 x)}{1331} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 80, normalized size = 0.82
method | result | size |
risch | \(\frac {\frac {1474169659425}{290521} x^{5}+\frac {9532963793295}{581042} x^{4}+\frac {6160937191623}{290521} x^{3}+\frac {15916809968421}{1162084} x^{2}+\frac {2568430130789}{581042} x +\frac {662695553413}{1162084}}{\left (2+3 x \right )^{4} \left (3+5 x \right )^{2}}-\frac {128 \ln \left (-1+2 x \right )}{22370117}-\frac {631722537 \ln \left (2+3 x \right )}{16807}+\frac {50028125 \ln \left (3+5 x \right )}{1331}\) | \(67\) |
norman | \(\frac {-\frac {623381628946173}{18593344} x^{4}-\frac {241099136633055}{9296672} x^{5}-\frac {151013201990311}{6972504} x^{3}-\frac {149106499517925}{18593344} x^{6}-\frac {146237616947111}{20917512} x^{2}-\frac {1572447355415}{1743126} x}{\left (2+3 x \right )^{4} \left (3+5 x \right )^{2}}-\frac {128 \ln \left (-1+2 x \right )}{22370117}-\frac {631722537 \ln \left (2+3 x \right )}{16807}+\frac {50028125 \ln \left (3+5 x \right )}{1331}\) | \(70\) |
default | \(-\frac {128 \ln \left (-1+2 x \right )}{22370117}+\frac {27}{28 \left (2+3 x \right )^{4}}+\frac {963}{49 \left (2+3 x \right )^{3}}+\frac {102114}{343 \left (2+3 x \right )^{2}}+\frac {11984706}{2401 \left (2+3 x \right )}-\frac {631722537 \ln \left (2+3 x \right )}{16807}-\frac {3125}{22 \left (3+5 x \right )^{2}}+\frac {509375}{121 \left (3+5 x \right )}+\frac {50028125 \ln \left (3+5 x \right )}{1331}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 84, normalized size = 0.87 \begin {gather*} \frac {5896678637700 \, x^{5} + 19065927586590 \, x^{4} + 24643748766492 \, x^{3} + 15916809968421 \, x^{2} + 5136860261578 \, x + 662695553413}{1162084 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} + \frac {50028125}{1331} \, \log \left (5 \, x + 3\right ) - \frac {631722537}{16807} \, \log \left (3 \, x + 2\right ) - \frac {128}{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. 173 vs.
\(2 (79) = 158\).
time = 1.30, size = 173, normalized size = 1.78 \begin {gather*} \frac {454044255102900 \, x^{5} + 1468076424167430 \, x^{4} + 1897568655019884 \, x^{3} + 1225594367568417 \, x^{2} + 3363290787500 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (5 \, x + 3\right ) - 3363290786988 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (3 \, x + 2\right ) - 512 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (2 \, x - 1\right ) + 395538240141506 \, x + 51027557612801}{89480468 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 87, normalized size = 0.90 \begin {gather*} - \frac {- 5896678637700 x^{5} - 19065927586590 x^{4} - 24643748766492 x^{3} - 15916809968421 x^{2} - 5136860261578 x - 662695553413}{2353220100 x^{6} + 9099117720 x^{5} + 14652717156 x^{4} + 12578397216 x^{3} + 6070726816 x^{2} + 1561840896 x + 167340096} - \frac {128 \log {\left (x - \frac {1}{2} \right )}}{22370117} + \frac {50028125 \log {\left (x + \frac {3}{5} \right )}}{1331} - \frac {631722537 \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 = 1.46, size = 91, normalized size = 0.94 \begin {gather*} \frac {11984706}{2401 \, {\left (3 \, x + 2\right )}} - \frac {46875 \, {\left (\frac {392}{3 \, x + 2} - 1795\right )}}{242 \, {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + \frac {102114}{343 \, {\left (3 \, x + 2\right )}^{2}} + \frac {963}{49 \, {\left (3 \, x + 2\right )}^{3}} + \frac {27}{28 \, {\left (3 \, x + 2\right )}^{4}} + \frac {50028125}{1331} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {128}{22370117} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 75, normalized size = 0.77 \begin {gather*} \frac {50028125\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {631722537\,\ln \left (x+\frac {2}{3}\right )}{16807}-\frac {128\,\ln \left (x-\frac {1}{2}\right )}{22370117}+\frac {\frac {727985017\,x^5}{290521}+\frac {70614546617\,x^4}{8715630}+\frac {76060952983\,x^3}{7263025}+\frac {5305603322807\,x^2}{784406700}+\frac {2568430130789\,x}{1176610050}+\frac {662695553413}{2353220100}}{x^6+\frac {58\,x^5}{15}+\frac {467\,x^4}{75}+\frac {3608\,x^3}{675}+\frac {5224\,x^2}{2025}+\frac {448\,x}{675}+\frac {16}{225}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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