Optimal. Leaf size=34 \[ \frac {\left (x-\left (x+\frac {1}{5} \log ^2\left (x^2\right )\right )^2\right )^2}{x \log \left (\frac {6}{5 x^2}\right )} \]
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Rubi [F]
time = 2.60, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{625} \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx\\ &=\frac {1}{625} \int \frac {\left (25 (-1+x) x+10 x \log ^2\left (x^2\right )+\log ^4\left (x^2\right )\right ) \left (\log \left (\frac {6}{5 x^2}\right ) \left (25 x (-1+3 x)+80 x \log \left (x^2\right )+10 x \log ^2\left (x^2\right )+16 \log ^3\left (x^2\right )-\log ^4\left (x^2\right )\right )+2 \left (25 (-1+x) x+10 x \log ^2\left (x^2\right )+\log ^4\left (x^2\right )\right )\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx\\ &=\frac {1}{625} \int \left (\frac {625 (-1+x) \left (-2+2 x-\log \left (\frac {6}{5 x^2}\right )+3 x \log \left (\frac {6}{5 x^2}\right )\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}+\frac {2000 (-1+x) \log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}+\frac {500 \left (-2+2 x-\log \left (\frac {6}{5 x^2}\right )+2 x \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}+\frac {400 (-1+3 x) \log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}+\frac {50 \left (-2+6 x+3 x \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {240 \log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}+\frac {40 \log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {16 \log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )}-\frac {\left (-2+\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )}\right ) \, dx\\ &=-\left (\frac {1}{625} \int \frac {\left (-2+\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx\right )+\frac {16}{625} \int \frac {\log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{125} \int \frac {\log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {2}{25} \int \frac {\left (-2+6 x+3 x \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {48}{125} \int \frac {\log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{25} \int \frac {(-1+3 x) \log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {4}{5} \int \frac {\left (-2+2 x-\log \left (\frac {6}{5 x^2}\right )+2 x \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{5} \int \frac {(-1+x) \log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\int \frac {(-1+x) \left (-2+2 x-\log \left (\frac {6}{5 x^2}\right )+3 x \log \left (\frac {6}{5 x^2}\right )\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx\\ &=-\left (\frac {1}{625} \int \left (-\frac {2 \log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {\log ^8\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )}\right ) \, dx\right )+\frac {16}{625} \int \frac {\log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{125} \int \frac {\log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {2}{25} \int \left (\frac {6 \log ^4\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}-\frac {2 \log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {3 \log ^4\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}\right ) \, dx+\frac {48}{125} \int \frac {\log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{25} \int \left (\frac {3 \log ^3\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}-\frac {\log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}\right ) \, dx+\frac {4}{5} \int \left (-\frac {2 \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}+\frac {2 x \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}-\frac {\log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}+\frac {2 x \log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}\right ) \, dx+\frac {16}{5} \int \left (-\frac {\log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}+\frac {x \log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}\right ) \, dx+\int \left (\frac {2 (-1+x)^2}{\log ^2\left (\frac {6}{5 x^2}\right )}+\frac {1-4 x+3 x^2}{\log \left (\frac {6}{5 x^2}\right )}\right ) \, dx\\ &=-\left (\frac {1}{625} \int \frac {\log ^8\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )} \, dx\right )+\frac {2}{625} \int \frac {\log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{625} \int \frac {\log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{125} \int \frac {\log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx-\frac {4}{25} \int \frac {\log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {6}{25} \int \frac {\log ^4\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {48}{125} \int \frac {\log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {12}{25} \int \frac {\log ^4\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx-\frac {16}{25} \int \frac {\log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx-\frac {4}{5} \int \frac {\log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx-\frac {8}{5} \int \frac {\log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{5} \int \frac {x \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{5} \int \frac {x \log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {48}{25} \int \frac {\log ^3\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+2 \int \frac {(-1+x)^2}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx-\frac {16}{5} \int \frac {\log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{5} \int \frac {x \log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\int \frac {1-4 x+3 x^2}{\log \left (\frac {6}{5 x^2}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(204\) vs. \(2(34)=68\).
time = 0.09, size = 204, normalized size = 6.00 \begin {gather*} \frac {1}{625} \left (-180 \log ^5\left (\frac {6}{5 x^2}\right )-600 \log ^4\left (\frac {6}{5 x^2}\right ) \left (\log (x)+\log \left (x^2\right )\right )-600 \log ^2\left (\frac {6}{5 x^2}\right ) \log (x) \left (-1+6 \log ^2\left (x^2\right )\right )-100 \log ^3\left (\frac {6}{5 x^2}\right ) \left (-1+24 \log (x) \log \left (x^2\right )+6 \log ^2\left (x^2\right )\right )+\frac {\left (25 (-1+x) x+10 x \log ^2\left (x^2\right )+\log ^4\left (x^2\right )\right )^2}{x \log \left (\frac {6}{5 x^2}\right )}-40 \log ^2\left (x^2\right ) \left (5 \log \left (x^2\right )-3 \log ^3\left (x^2\right )+15 \log (x) \left (-1+\log ^2\left (x^2\right )\right )\right )+300 \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right ) \left (\log (x) \left (4-8 \log ^2\left (x^2\right )\right )+\log \left (x^2\right ) \left (-1+\log ^2\left (x^2\right )\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 30.14, size = 35897, normalized size = 1055.79
method | result | size |
risch | \(\text {Expression too large to display}\) | \(35897\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 627 vs.
\(2 (31) = 62\).
time = 0.55, size = 627, normalized size = 18.44 \begin {gather*} -\frac {256 \, \log \left (x\right )^{8} + 1280 \, x \log \left (x\right )^{6} + 800 \, {\left (3 \, x^{2} - x\right )} \log \left (x\right )^{4} + 625 \, x^{4} - 1250 \, x^{3} + 20 \, {\left (2 \, \log \left (5\right )^{5} + 10 \, \log \left (5\right ) \log \left (3\right )^{4} - 2 \, \log \left (3\right )^{5} + 10 \, {\left (\log \left (5\right ) - \log \left (3\right )\right )} \log \left (2\right )^{4} - 2 \, \log \left (2\right )^{5} - 5 \, {\left (4 \, \log \left (5\right )^{2} - 1\right )} \log \left (3\right )^{3} - 5 \, {\left (4 \, \log \left (5\right )^{2} - 8 \, \log \left (5\right ) \log \left (3\right ) + 4 \, \log \left (3\right )^{2} - 1\right )} \log \left (2\right )^{3} - 5 \, \log \left (5\right )^{3} + 5 \, {\left (4 \, \log \left (5\right )^{3} - 3 \, \log \left (5\right )\right )} \log \left (3\right )^{2} + 5 \, {\left (4 \, \log \left (5\right )^{3} + 12 \, \log \left (5\right ) \log \left (3\right )^{2} - 4 \, \log \left (3\right )^{3} - 3 \, {\left (4 \, \log \left (5\right )^{2} - 1\right )} \log \left (3\right ) - 3 \, \log \left (5\right )\right )} \log \left (2\right )^{2} - 5 \, {\left (2 \, \log \left (5\right )^{4} - 3 \, \log \left (5\right )^{2}\right )} \log \left (3\right ) - 5 \, {\left (2 \, \log \left (5\right )^{4} - 8 \, \log \left (5\right ) \log \left (3\right )^{3} + 2 \, \log \left (3\right )^{4} + 3 \, {\left (4 \, \log \left (5\right )^{2} - 1\right )} \log \left (3\right )^{2} - 3 \, \log \left (5\right )^{2} - 2 \, {\left (4 \, \log \left (5\right )^{3} - 3 \, \log \left (5\right )\right )} \log \left (3\right )\right )} \log \left (2\right )\right )} x \log \left (x\right ) + 2000 \, {\left (x^{3} - x^{2}\right )} \log \left (x\right )^{2} + 10 \, {\left (2 \, \log \left (5\right )^{6} - 12 \, \log \left (5\right ) \log \left (3\right )^{5} + 2 \, \log \left (3\right )^{6} - 12 \, {\left (\log \left (5\right ) - \log \left (3\right )\right )} \log \left (2\right )^{5} + 2 \, \log \left (2\right )^{6} + 5 \, {\left (6 \, \log \left (5\right )^{2} - 1\right )} \log \left (3\right )^{4} + 5 \, {\left (6 \, \log \left (5\right )^{2} - 12 \, \log \left (5\right ) \log \left (3\right ) + 6 \, \log \left (3\right )^{2} - 1\right )} \log \left (2\right )^{4} - 5 \, \log \left (5\right )^{4} - 20 \, {\left (2 \, \log \left (5\right )^{3} - \log \left (5\right )\right )} \log \left (3\right )^{3} - 20 \, {\left (2 \, \log \left (5\right )^{3} + 6 \, \log \left (5\right ) \log \left (3\right )^{2} - 2 \, \log \left (3\right )^{3} - {\left (6 \, \log \left (5\right )^{2} - 1\right )} \log \left (3\right ) - \log \left (5\right )\right )} \log \left (2\right )^{3} + 30 \, {\left (\log \left (5\right )^{4} - \log \left (5\right )^{2}\right )} \log \left (3\right )^{2} + 30 \, {\left (\log \left (5\right )^{4} - 4 \, \log \left (5\right ) \log \left (3\right )^{3} + \log \left (3\right )^{4} + {\left (6 \, \log \left (5\right )^{2} - 1\right )} \log \left (3\right )^{2} - \log \left (5\right )^{2} - 2 \, {\left (2 \, \log \left (5\right )^{3} - \log \left (5\right )\right )} \log \left (3\right )\right )} \log \left (2\right )^{2} - 4 \, {\left (3 \, \log \left (5\right )^{5} - 5 \, \log \left (5\right )^{3}\right )} \log \left (3\right ) - 4 \, {\left (3 \, \log \left (5\right )^{5} + 15 \, \log \left (5\right ) \log \left (3\right )^{4} - 3 \, \log \left (3\right )^{5} - 5 \, {\left (6 \, \log \left (5\right )^{2} - 1\right )} \log \left (3\right )^{3} - 5 \, \log \left (5\right )^{3} + 15 \, {\left (2 \, \log \left (5\right )^{3} - \log \left (5\right )\right )} \log \left (3\right )^{2} - 15 \, {\left (\log \left (5\right )^{4} - \log \left (5\right )^{2}\right )} \log \left (3\right )\right )} \log \left (2\right )\right )} x + 625 \, x^{2}}{625 \, {\left (x {\left (\log \left (5\right ) - \log \left (3\right ) - \log \left (2\right )\right )} + 2 \, x \log \left (x\right )\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. 285 vs.
\(2 (31) = 62\).
time = 0.37, size = 285, normalized size = 8.38 \begin {gather*} \frac {\log \left (\frac {6}{5}\right )^{8} - 8 \, \log \left (\frac {6}{5}\right ) \log \left (\frac {6}{5 \, x^{2}}\right )^{7} + \log \left (\frac {6}{5 \, x^{2}}\right )^{8} + 20 \, x \log \left (\frac {6}{5}\right )^{6} + 4 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{2} + 5 \, x\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{6} - 8 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{3} + 15 \, x \log \left (\frac {6}{5}\right )\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{5} + 50 \, {\left (3 \, x^{2} - x\right )} \log \left (\frac {6}{5}\right )^{4} + 10 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{4} + 30 \, x \log \left (\frac {6}{5}\right )^{2} + 15 \, x^{2} - 5 \, x\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{4} + 625 \, x^{4} - 8 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{5} + 50 \, x \log \left (\frac {6}{5}\right )^{3} + 25 \, {\left (3 \, x^{2} - x\right )} \log \left (\frac {6}{5}\right )\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{3} - 1250 \, x^{3} + 500 \, {\left (x^{3} - x^{2}\right )} \log \left (\frac {6}{5}\right )^{2} + 4 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{6} + 75 \, x \log \left (\frac {6}{5}\right )^{4} + 125 \, x^{3} + 75 \, {\left (3 \, x^{2} - x\right )} \log \left (\frac {6}{5}\right )^{2} - 125 \, x^{2}\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{2} + 625 \, x^{2} - 8 \, {\left (\log \left (\frac {6}{5}\right )^{7} + 75 \, x^{2} \log \left (\frac {6}{5}\right )^{3} + 125 \, {\left (x^{3} - x^{2}\right )} \log \left (\frac {6}{5}\right )\right )} \log \left (\frac {6}{5 \, x^{2}}\right )}{625 \, x \log \left (\frac {6}{5 \, x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 1028 vs.
\(2 (24) = 48\).
time = 1.52, size = 1028, normalized size = 30.24 \begin {gather*} \frac {x^{2} \left (- 500 \log {\left (6 \right )} + 500 \log {\left (5 \right )}\right )}{625} + \frac {x \left (- 450 \log {\left (5 \right )}^{2} \log {\left (6 \right )} - 150 \log {\left (6 \right )}^{3} - 500 \log {\left (5 \right )} + 150 \log {\left (5 \right )}^{3} + 500 \log {\left (6 \right )} + 450 \log {\left (5 \right )} \log {\left (6 \right )}^{2}\right )}{625} - \frac {4 \left (- \log {\left (6 \right )} + \log {\left (5 \right )}\right )^{2} \left (- 4 \log {\left (5 \right )} \log {\left (6 \right )} - 5 + 2 \log {\left (5 \right )}^{2} + 2 \log {\left (6 \right )}^{2}\right ) \log {\left (x \right )}}{125} + \frac {- 625 x^{4} - 500 x^{3} \log {\left (6 \right )}^{2} - 500 x^{3} \log {\left (5 \right )}^{2} + 1250 x^{3} + 1000 x^{3} \log {\left (5 \right )} \log {\left (6 \right )} - 900 x^{2} \log {\left (5 \right )}^{2} \log {\left (6 \right )}^{2} - 1000 x^{2} \log {\left (5 \right )} \log {\left (6 \right )} - 150 x^{2} \log {\left (6 \right )}^{4} - 150 x^{2} \log {\left (5 \right )}^{4} - 625 x^{2} + 500 x^{2} \log {\left (5 \right )}^{2} + 500 x^{2} \log {\left (6 \right )}^{2} + 600 x^{2} \log {\left (5 \right )}^{3} \log {\left (6 \right )} + 600 x^{2} \log {\left (5 \right )} \log {\left (6 \right )}^{3} - 300 x \log {\left (5 \right )}^{2} \log {\left (6 \right )}^{4} - 300 x \log {\left (5 \right )}^{4} \log {\left (6 \right )}^{2} - 200 x \log {\left (5 \right )} \log {\left (6 \right )}^{3} - 200 x \log {\left (5 \right )}^{3} \log {\left (6 \right )} - 20 x \log {\left (6 \right )}^{6} - 20 x \log {\left (5 \right )}^{6} + 50 x \log {\left (5 \right )}^{4} + 50 x \log {\left (6 \right )}^{4} + 120 x \log {\left (5 \right )}^{5} \log {\left (6 \right )} + 300 x \log {\left (5 \right )}^{2} \log {\left (6 \right )}^{2} + 120 x \log {\left (5 \right )} \log {\left (6 \right )}^{5} + 400 x \log {\left (5 \right )}^{3} \log {\left (6 \right )}^{3} - 70 \log {\left (5 \right )}^{4} \log {\left (6 \right )}^{4} - 28 \log {\left (5 \right )}^{2} \log {\left (6 \right )}^{6} - 28 \log {\left (5 \right )}^{6} \log {\left (6 \right )}^{2} - \log {\left (6 \right )}^{8} - \log {\left (5 \right )}^{8} + 8 \log {\left (5 \right )}^{7} \log {\left (6 \right )} + 8 \log {\left (5 \right )} \log {\left (6 \right )}^{7} + 56 \log {\left (5 \right )}^{5} \log {\left (6 \right )}^{3} + 56 \log {\left (5 \right )}^{3} \log {\left (6 \right )}^{5}}{625 x \log {\left (x^{2} \right )} - 625 x \log {\left (6 \right )} + 625 x \log {\left (5 \right )}} + \frac {\left (- 20 x - \log {\left (6 \right )}^{2} - \log {\left (5 \right )}^{2} + 2 \log {\left (5 \right )} \log {\left (6 \right )}\right ) \log {\left (x^{2} \right )}^{5}}{625 x} + \frac {\left (- 20 x \log {\left (6 \right )} + 20 x \log {\left (5 \right )} - 3 \log {\left (5 \right )}^{2} \log {\left (6 \right )} - \log {\left (6 \right )}^{3} + \log {\left (5 \right )}^{3} + 3 \log {\left (5 \right )} \log {\left (6 \right )}^{2}\right ) \log {\left (x^{2} \right )}^{4}}{625 x} + \frac {\left (- 150 x^{2} - 20 x \log {\left (6 \right )}^{2} - 20 x \log {\left (5 \right )}^{2} + 50 x + 40 x \log {\left (5 \right )} \log {\left (6 \right )} - 6 \log {\left (5 \right )}^{2} \log {\left (6 \right )}^{2} - \log {\left (6 \right )}^{4} - \log {\left (5 \right )}^{4} + 4 \log {\left (5 \right )}^{3} \log {\left (6 \right )} + 4 \log {\left (5 \right )} \log {\left (6 \right )}^{3}\right ) \log {\left (x^{2} \right )}^{3}}{625 x} + \frac {\left (- 500 x^{3} - 150 x^{2} \log {\left (6 \right )}^{2} - 150 x^{2} \log {\left (5 \right )}^{2} + 500 x^{2} + 300 x^{2} \log {\left (5 \right )} \log {\left (6 \right )} - 15 \log {\left (5 \right )}^{2} \log {\left (6 \right )}^{4} - 15 \log {\left (5 \right )}^{4} \log {\left (6 \right )}^{2} - \log {\left (6 \right )}^{6} - \log {\left (5 \right )}^{6} + 6 \log {\left (5 \right )}^{5} \log {\left (6 \right )} + 6 \log {\left (5 \right )} \log {\left (6 \right )}^{5} + 20 \log {\left (5 \right )}^{3} \log {\left (6 \right )}^{3}\right ) \log {\left (x^{2} \right )}}{625 x} + \frac {\left (- 150 x^{2} \log {\left (6 \right )} + 150 x^{2} \log {\left (5 \right )} - 60 x \log {\left (5 \right )}^{2} \log {\left (6 \right )} - 20 x \log {\left (6 \right )}^{3} - 50 x \log {\left (5 \right )} + 20 x \log {\left (5 \right )}^{3} + 50 x \log {\left (6 \right )} + 60 x \log {\left (5 \right )} \log {\left (6 \right )}^{2} - 10 \log {\left (5 \right )}^{2} \log {\left (6 \right )}^{3} - 5 \log {\left (5 \right )}^{4} \log {\left (6 \right )} - \log {\left (6 \right )}^{5} + \log {\left (5 \right )}^{5} + 5 \log {\left (5 \right )} \log {\left (6 \right )}^{4} + 10 \log {\left (5 \right )}^{3} \log {\left (6 \right )}^{2}\right ) \log {\left (x^{2} \right )}^{2}}{625 x} - \frac {\log {\left (x^{2} \right )}^{7}}{625 x} + \frac {\left (- \log {\left (6 \right )} + \log {\left (5 \right )}\right ) \log {\left (x^{2} \right )}^{6}}{625 x} + \frac {- 35 \log {\left (5 \right )}^{4} \log {\left (6 \right )}^{3} - 21 \log {\left (5 \right )}^{2} \log {\left (6 \right )}^{5} - 7 \log {\left (5 \right )}^{6} \log {\left (6 \right )} - \log {\left (6 \right )}^{7} + \log {\left (5 \right )}^{7} + 7 \log {\left (5 \right )} \log {\left (6 \right )}^{6} + 21 \log {\left (5 \right )}^{5} \log {\left (6 \right )}^{2} + 35 \log {\left (5 \right )}^{3} \log {\left (6 \right )}^{4}}{625 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.11, size = 520, normalized size = 15.29 \begin {gather*} -\frac {\frac {1000\,x^3\,{\ln \left (\frac {6}{5}\right )}^2-500\,x^2\,{\ln \left (\frac {6}{5}\right )}^3-1000\,x^2\,{\ln \left (\frac {6}{5}\right )}^2+300\,x^2\,{\ln \left (\frac {6}{5}\right )}^4+1000\,x^3\,{\ln \left (\frac {6}{5}\right )}^3+150\,x^2\,{\ln \left (\frac {6}{5}\right )}^5+625\,x^2\,\ln \left (\frac {6}{5}\right )-2500\,x^3\,\ln \left (\frac {6}{5}\right )-100\,x\,{\ln \left (\frac {6}{5}\right )}^4+1875\,x^4\,\ln \left (\frac {6}{5}\right )+40\,x\,{\ln \left (\frac {6}{5}\right )}^6+2\,{\ln \left (\frac {6}{5}\right )}^8-{\ln \left (\frac {6}{5}\right )}^9+1250\,x^2-2500\,x^3+1250\,x^4}{1250\,x}-\frac {\ln \left (x^2\right )\,\left (1000\,x^3\,{\ln \left (\frac {6}{5}\right )}^2-500\,x^2\,{\ln \left (\frac {6}{5}\right )}^2+150\,x^2\,{\ln \left (\frac {6}{5}\right )}^4-{\ln \left (\frac {6}{5}\right )}^8+625\,x^2-2500\,x^3+1875\,x^4\right )}{1250\,x}}{\ln \left (x^2\right )-\ln \left (\frac {6}{5}\right )}-{\ln \left (x^2\right )}^2\,\left (\frac {182\,\ln \left (\frac {6}{5}\right )}{125}+\frac {\frac {6\,\ln \left (\frac {6}{5}\right )\,x^2}{25}+\left (-\frac {192\,\ln \left (\frac {6}{5}\right )}{125}-\frac {24\,{\ln \left (\frac {6}{5}\right )}^2}{125}-\frac {372}{25}\right )\,x+\frac {{\ln \left (\frac {6}{5}\right )}^5}{625}}{x}+\frac {24\,{\ln \left (\frac {6}{5}\right )}^2}{125}+\frac {4\,{\ln \left (\frac {6}{5}\right )}^3}{125}+\frac {372}{25}\right )-{\ln \left (x^2\right )}^3\,\left (\frac {32\,\ln \left (\frac {6}{5}\right )}{125}+\frac {4\,{\ln \left (\frac {6}{5}\right )}^2}{125}+\frac {\frac {6\,x^2}{25}+\left (-\frac {32\,\ln \left (\frac {6}{5}\right )}{125}-\frac {64}{25}\right )\,x+\frac {{\ln \left (\frac {6}{5}\right )}^4}{625}}{x}+\frac {62}{25}\right )-{\ln \left (x^2\right )}^5\,\left (\frac {{\ln \left (\frac {6}{5}\right )}^2}{625\,x}+\frac {4}{125}\right )-x\,\left (\frac {6\,{\ln \left (\frac {6}{5}\right )}^3}{25}-\frac {2\,{\ln \left (\frac {6}{5}\right )}^2}{5}-\frac {4\,\ln \left (\frac {6}{5}\right )}{5}+\frac {3\,{\ln \left (\frac {6}{5}\right )}^4}{25}+\frac {1}{2}\right )-x^2\,\left (\frac {4\,\ln \left (\frac {6}{5}\right )}{5}+\frac {4\,{\ln \left (\frac {6}{5}\right )}^2}{5}-2\right )-{\ln \left (x^2\right )}^4\,\left (\frac {4\,\ln \left (\frac {6}{5}\right )}{125}-\frac {\frac {8\,x}{25}-\frac {{\ln \left (\frac {6}{5}\right )}^3}{625}}{x}+\frac {8}{25}\right )-\frac {3\,x^3}{2}-\frac {{\ln \left (x^2\right )}^7}{625\,x}-\frac {\frac {{\ln \left (\frac {6}{5}\right )}^7}{625}-\frac {{\ln \left (\frac {6}{5}\right )}^8}{1250}}{x}-\ln \left (x\right )\,\left (\frac {1456\,\ln \left (\frac {6}{5}\right )}{125}+\frac {172\,{\ln \left (\frac {6}{5}\right )}^2}{125}+\frac {32\,{\ln \left (\frac {6}{5}\right )}^3}{125}+\frac {8\,{\ln \left (\frac {6}{5}\right )}^4}{125}+\frac {2976}{25}\right )-\frac {{\ln \left (x^2\right )}^6\,\ln \left (\frac {6}{5}\right )}{625\,x}-\frac {\ln \left (x^2\right )\,\left (\frac {4\,x^3}{5}+\left (\frac {6\,{\ln \left (\frac {6}{5}\right )}^2}{25}-\frac {4}{5}\right )\,x^2+\left (-\frac {728\,\ln \left (\frac {6}{5}\right )}{125}-\frac {96\,{\ln \left (\frac {6}{5}\right )}^2}{125}-\frac {16\,{\ln \left (\frac {6}{5}\right )}^3}{125}-\frac {1488}{25}\right )\,x+\frac {{\ln \left (\frac {6}{5}\right )}^6}{625}\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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