Optimal. Leaf size=29 \[ \left (-4+\frac {2 \left (-1+\frac {x}{-\log (2)+\log (3)}+\log (-x+\log (5))\right )}{x}\right )^2 \]
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Rubi [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 0.68, antiderivative size = 404, normalized size of antiderivative = 13.93, number of steps
used = 27, number of rules used = 20, integrand size = 181, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.110, Rules used = {6, 6820, 12,
6874, 147, 2465, 2442, 46, 2439, 2438, 2437, 2338, 36, 29, 31, 2445, 2458, 2389, 2379, 2351}
\begin {gather*} \frac {8 \text {Li}_2\left (\frac {x}{\log (5)}\right )}{\log ^2(5)}-\frac {8 \text {Li}_2\left (-\frac {\log (5)}{x-\log (5)}\right )}{\log ^2(5)}+\frac {4}{x^2}+\frac {4 \log ^2(\log (5)-x)}{x^2}-\frac {4 \log \left (\frac {9}{4}\right ) \log (\log (5)-x)}{x^2 \log \left (\frac {3}{2}\right )}+\frac {4 \log ^2(\log (5)-x)}{\log ^2(5)}+\frac {8 \log \left (\frac {\log (5)}{x-\log (5)}+1\right ) \log (\log (5)-x)}{\log ^2(5)}+\frac {8 (x-\log (5)) \log (\log (5)-x)}{x \log ^2(5)}-\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {4 \log \left (\frac {9}{4}\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {8 \log (x)}{\log ^2(5)}+\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {4 \log \left (\frac {9}{4}\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {8 \log (\log (5)) \log (x)}{\log ^2(5)}-\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (\log (5)-x)}{x \log \left (\frac {3}{2}\right ) \log (5)}+\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )}{x \log \left (\frac {3}{2}\right ) \log (5)}+\frac {4 \log \left (\frac {9}{4}\right )}{x \log \left (\frac {3}{2}\right ) \log (5)} \end {gather*}
Warning: Unable to verify antiderivative.
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Rule 6
Rule 12
Rule 29
Rule 31
Rule 36
Rule 46
Rule 147
Rule 2338
Rule 2351
Rule 2379
Rule 2389
Rule 2437
Rule 2438
Rule 2439
Rule 2442
Rule 2445
Rule 2458
Rule 2465
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-16 x^2+\left (-16 x-32 x^2\right ) \log (2)+\left (16 x+32 x^2\right ) \log (3)+(8 x+(8+16 x) \log (2)+(-8-16 x) \log (3)) \log (5)+\left (8 x^2+\left (24 x+16 x^2\right ) \log (2)+\left (-24 x-16 x^2\right ) \log (3)+(-8 x+(-16-16 x) \log (2)+(16+16 x) \log (3)) \log (5)\right ) \log (-x+\log (5))+(-8 x \log (2)+8 x \log (3)+(8 \log (2)-8 \log (3)) \log (5)) \log ^2(-x+\log (5))}{x^4 (\log (2)-\log (3))+\left (-x^3 \log (2)+x^3 \log (3)\right ) \log (5)} \, dx\\ &=\int \frac {8 \left (\log \left (\frac {3}{2}\right )+x \left (-1+\log \left (\frac {9}{4}\right )\right )-\log \left (\frac {3}{2}\right ) \log (-x+\log (5))\right ) (-2 x+\log (5)+(x-\log (5)) \log (-x+\log (5)))}{x^3 \log \left (\frac {3}{2}\right ) (x-\log (5))} \, dx\\ &=\frac {8 \int \frac {\left (\log \left (\frac {3}{2}\right )+x \left (-1+\log \left (\frac {9}{4}\right )\right )-\log \left (\frac {3}{2}\right ) \log (-x+\log (5))\right ) (-2 x+\log (5)+(x-\log (5)) \log (-x+\log (5)))}{x^3 (x-\log (5))} \, dx}{\log \left (\frac {3}{2}\right )}\\ &=\frac {8 \int \left (\frac {\left (\log \left (\frac {3}{2}\right )-x \left (1-\log \left (\frac {9}{4}\right )\right )\right ) (-2 x+\log (5))}{x^3 (x-\log (5))}+\frac {\left (-x^2 \left (1-\log \left (\frac {9}{4}\right )\right )-\log \left (\frac {9}{4}\right ) \log (5)-x \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {135}{8}\right )\right )\right ) \log (-x+\log (5))}{x^3 (x-\log (5))}-\frac {\log \left (\frac {3}{2}\right ) \log ^2(-x+\log (5))}{x^3}\right ) \, dx}{\log \left (\frac {3}{2}\right )}\\ &=-\left (8 \int \frac {\log ^2(-x+\log (5))}{x^3} \, dx\right )+\frac {8 \int \frac {\left (\log \left (\frac {3}{2}\right )+x \left (-1+\log \left (\frac {9}{4}\right )\right )\right ) (-2 x+\log (5))}{x^3 (x-\log (5))} \, dx}{\log \left (\frac {3}{2}\right )}+\frac {8 \int \frac {\left (-x^2 \left (1-\log \left (\frac {9}{4}\right )\right )-\log \left (\frac {9}{4}\right ) \log (5)-x \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {135}{8}\right )\right )\right ) \log (-x+\log (5))}{x^3 (x-\log (5))} \, dx}{\log \left (\frac {3}{2}\right )}\\ &=\frac {4 \log ^2(-x+\log (5))}{x^2}+8 \int \frac {\log (-x+\log (5))}{x^2 (-x+\log (5))} \, dx+\frac {8 \int \left (-\frac {\log \left (\frac {3}{2}\right )}{x^3}+\frac {\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)}{(x-\log (5)) \log ^2(5)}+\frac {-\log \left (\frac {10}{3}\right )+\log \left (\frac {9}{4}\right ) \log (5)}{x \log ^2(5)}+\frac {-\log \left (\frac {9}{4}\right ) \log (5)+\log \left (\frac {15}{2}\right )}{x^2 \log (5)}\right ) \, dx}{\log \left (\frac {3}{2}\right )}+\frac {8 \int \left (\frac {\log \left (\frac {9}{4}\right ) \log (-x+\log (5))}{x^3}-\frac {\log \left (\frac {3}{2}\right ) \log (-x+\log (5))}{x \log ^2(5)}+\frac {\log \left (\frac {3}{2}\right ) \log (-x+\log (5))}{(x-\log (5)) \log ^2(5)}+\frac {\left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (-x+\log (5))}{x^2 \log (5)}\right ) \, dx}{\log \left (\frac {3}{2}\right )}\\ &=\frac {4}{x^2}+\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )}{x \log \left (\frac {3}{2}\right ) \log (5)}-\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {4 \log ^2(-x+\log (5))}{x^2}-8 \text {Subst}\left (\int \frac {\log (x)}{x (-x+\log (5))^2} \, dx,x,-x+\log (5)\right )+\frac {\left (8 \log \left (\frac {9}{4}\right )\right ) \int \frac {\log (-x+\log (5))}{x^3} \, dx}{\log \left (\frac {3}{2}\right )}-\frac {8 \int \frac {\log (-x+\log (5))}{x} \, dx}{\log ^2(5)}+\frac {8 \int \frac {\log (-x+\log (5))}{x-\log (5)} \, dx}{\log ^2(5)}+\frac {\left (8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )\right ) \int \frac {\log (-x+\log (5))}{x^2} \, dx}{\log \left (\frac {3}{2}\right ) \log (5)}\\ &=\frac {4}{x^2}+\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )}{x \log \left (\frac {3}{2}\right ) \log (5)}-\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {8 \log (x) \log (\log (5))}{\log ^2(5)}-\frac {4 \log \left (\frac {9}{4}\right ) \log (-x+\log (5))}{x^2 \log \left (\frac {3}{2}\right )}-\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (-x+\log (5))}{x \log \left (\frac {3}{2}\right ) \log (5)}+\frac {4 \log ^2(-x+\log (5))}{x^2}-\frac {\left (4 \log \left (\frac {9}{4}\right )\right ) \int \frac {1}{x^2 (-x+\log (5))} \, dx}{\log \left (\frac {3}{2}\right )}-\frac {8 \int \frac {\log \left (1-\frac {x}{\log (5)}\right )}{x} \, dx}{\log ^2(5)}+\frac {8 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,-x+\log (5)\right )}{\log ^2(5)}-\frac {8 \text {Subst}\left (\int \frac {\log (x)}{(-x+\log (5))^2} \, dx,x,-x+\log (5)\right )}{\log (5)}-\frac {8 \text {Subst}\left (\int \frac {\log (x)}{x (-x+\log (5))} \, dx,x,-x+\log (5)\right )}{\log (5)}-\frac {\left (8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )\right ) \int \frac {1}{x (-x+\log (5))} \, dx}{\log \left (\frac {3}{2}\right ) \log (5)}\\ &=\frac {4}{x^2}+\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )}{x \log \left (\frac {3}{2}\right ) \log (5)}-\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {8 \log (x) \log (\log (5))}{\log ^2(5)}-\frac {4 \log \left (\frac {9}{4}\right ) \log (-x+\log (5))}{x^2 \log \left (\frac {3}{2}\right )}+\frac {8 (x-\log (5)) \log (-x+\log (5))}{x \log ^2(5)}-\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (-x+\log (5))}{x \log \left (\frac {3}{2}\right ) \log (5)}+\frac {4 \log ^2(-x+\log (5))}{x^2}+\frac {4 \log ^2(-x+\log (5))}{\log ^2(5)}+\frac {8 \text {Li}_2\left (\frac {x}{\log (5)}\right )}{\log ^2(5)}-\frac {\left (4 \log \left (\frac {9}{4}\right )\right ) \int \left (\frac {1}{x \log ^2(5)}-\frac {1}{(x-\log (5)) \log ^2(5)}+\frac {1}{x^2 \log (5)}\right ) \, dx}{\log \left (\frac {3}{2}\right )}+\frac {8 \text {Subst}\left (\int \frac {1}{-x+\log (5)} \, dx,x,-x+\log (5)\right )}{\log ^2(5)}-\frac {8 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,-x+\log (5)\right )}{\log ^2(5)}-\frac {8 \text {Subst}\left (\int \frac {\log (x)}{-x+\log (5)} \, dx,x,-x+\log (5)\right )}{\log ^2(5)}-\frac {\left (8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )\right ) \int \frac {1}{x} \, dx}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {\left (8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )\right ) \int \frac {1}{-x+\log (5)} \, dx}{\log \left (\frac {3}{2}\right ) \log ^2(5)}\\ &=\frac {4}{x^2}+\frac {4 \log \left (\frac {9}{4}\right )}{x \log \left (\frac {3}{2}\right ) \log (5)}+\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )}{x \log \left (\frac {3}{2}\right ) \log (5)}-\frac {8 \log (x)}{\log ^2(5)}-\frac {4 \log \left (\frac {9}{4}\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {4 \log \left (\frac {9}{4}\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {4 \log \left (\frac {9}{4}\right ) \log (-x+\log (5))}{x^2 \log \left (\frac {3}{2}\right )}+\frac {8 (x-\log (5)) \log (-x+\log (5))}{x \log ^2(5)}-\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (-x+\log (5))}{x \log \left (\frac {3}{2}\right ) \log (5)}+\frac {4 \log ^2(-x+\log (5))}{x^2}+\frac {8 \text {Li}_2\left (\frac {x}{\log (5)}\right )}{\log ^2(5)}-\frac {8 \text {Subst}\left (\int \frac {\log \left (\frac {x}{\log (5)}\right )}{-x+\log (5)} \, dx,x,-x+\log (5)\right )}{\log ^2(5)}\\ &=\frac {4}{x^2}+\frac {4 \log \left (\frac {9}{4}\right )}{x \log \left (\frac {3}{2}\right ) \log (5)}+\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right )}{x \log \left (\frac {3}{2}\right ) \log (5)}-\frac {8 \log (x)}{\log ^2(5)}-\frac {4 \log \left (\frac {9}{4}\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (x)}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {4 \log \left (\frac {9}{4}\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {8 \left (\log \left (\frac {10}{3}\right )-\log \left (\frac {9}{4}\right ) \log (5)\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}+\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (x-\log (5))}{\log \left (\frac {3}{2}\right ) \log ^2(5)}-\frac {4 \log \left (\frac {9}{4}\right ) \log (-x+\log (5))}{x^2 \log \left (\frac {3}{2}\right )}+\frac {8 (x-\log (5)) \log (-x+\log (5))}{x \log ^2(5)}-\frac {8 \left (\log \left (\frac {9}{4}\right ) \log (5)-\log \left (\frac {15}{2}\right )\right ) \log (-x+\log (5))}{x \log \left (\frac {3}{2}\right ) \log (5)}+\frac {4 \log ^2(-x+\log (5))}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.15, size = 47, normalized size = 1.62 \begin {gather*} -\frac {4 (-1+\log (-x+\log (5))) \left (\log \left (\frac {3}{2}\right )+2 x \left (-1+\log \left (\frac {9}{4}\right )\right )-\log \left (\frac {3}{2}\right ) \log (-x+\log (5))\right )}{x^2 \log \left (\frac {3}{2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(77\) vs.
\(2(29)=58\).
time = 1.54, size = 78, normalized size = 2.69
method | result | size |
norman | \(\frac {4+4 \ln \left (\ln \left (5\right )-x \right )^{2}+\frac {8 \left (2 \ln \left (3\right )-2 \ln \left (2\right )-1\right ) x}{\ln \left (3\right )-\ln \left (2\right )}-\frac {8 \left (2 \ln \left (3\right )-2 \ln \left (2\right )-1\right ) x \ln \left (\ln \left (5\right )-x \right )}{\ln \left (3\right )-\ln \left (2\right )}-8 \ln \left (\ln \left (5\right )-x \right )}{x^{2}}\) | \(78\) |
risch | \(\frac {4 \ln \left (\ln \left (5\right )-x \right )^{2}}{x^{2}}-\frac {8 \left (2 x \ln \left (3\right )-2 x \ln \left (2\right )+\ln \left (3\right )-\ln \left (2\right )-x \right ) \ln \left (\ln \left (5\right )-x \right )}{\left (\ln \left (3\right )-\ln \left (2\right )\right ) x^{2}}+\frac {16 x \ln \left (3\right )-16 x \ln \left (2\right )+4 \ln \left (3\right )-4 \ln \left (2\right )-8 x}{\left (\ln \left (3\right )-\ln \left (2\right )\right ) x^{2}}\) | \(91\) |
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. 295 vs.
\(2 (30) = 60\).
time = 0.51, size = 295, normalized size = 10.17 \begin {gather*} 4 \, {\left (\frac {2 \, \log \left (x - \log \left (5\right )\right )}{{\left (\log \left (3\right ) - \log \left (2\right )\right )} \log \left (5\right )^{3}} - \frac {2 \, \log \left (x\right )}{{\left (\log \left (3\right ) - \log \left (2\right )\right )} \log \left (5\right )^{3}} + \frac {2 \, x + \log \left (5\right )}{x^{2} {\left (\log \left (3\right ) - \log \left (2\right )\right )} \log \left (5\right )^{2}}\right )} \log \left (5\right ) \log \left (3\right ) - 4 \, {\left (\frac {2 \, \log \left (x - \log \left (5\right )\right )}{{\left (\log \left (3\right ) - \log \left (2\right )\right )} \log \left (5\right )^{3}} - \frac {2 \, \log \left (x\right )}{{\left (\log \left (3\right ) - \log \left (2\right )\right )} \log \left (5\right )^{3}} + \frac {2 \, x + \log \left (5\right )}{x^{2} {\left (\log \left (3\right ) - \log \left (2\right )\right )} \log \left (5\right )^{2}}\right )} \log \left (5\right ) \log \left (2\right ) + \frac {8 \, \log \left (x\right )}{\log \left (5\right )^{2}} + \frac {4 \, {\left ({\left (\log \left (5\right )^{2} \log \left (3\right ) - \log \left (5\right )^{2} \log \left (2\right )\right )} \log \left (-x + \log \left (5\right )\right )^{2} - 2 \, {\left (\log \left (5\right )^{2} - {\left (2 \, \log \left (5\right )^{2} - \log \left (5\right )\right )} \log \left (3\right ) + {\left (2 \, \log \left (5\right )^{2} - \log \left (5\right )\right )} \log \left (2\right )\right )} x - 2 \, {\left (x^{2} {\left (\log \left (3\right ) - \log \left (2\right )\right )} + \log \left (5\right )^{2} \log \left (3\right ) - \log \left (5\right )^{2} \log \left (2\right ) + {\left (2 \, \log \left (5\right )^{2} \log \left (3\right ) - 2 \, \log \left (5\right )^{2} \log \left (2\right ) - \log \left (5\right )^{2}\right )} x\right )} \log \left (-x + \log \left (5\right )\right )\right )}}{{\left (\log \left (5\right )^{2} \log \left (3\right ) - \log \left (5\right )^{2} \log \left (2\right )\right )} x^{2}} \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. 86 vs.
\(2 (30) = 60\).
time = 0.35, size = 86, normalized size = 2.97 \begin {gather*} \frac {4 \, {\left ({\left (\log \left (3\right ) - \log \left (2\right )\right )} \log \left (-x + \log \left (5\right )\right )^{2} + {\left (4 \, x + 1\right )} \log \left (3\right ) - {\left (4 \, x + 1\right )} \log \left (2\right ) - 2 \, {\left ({\left (2 \, x + 1\right )} \log \left (3\right ) - {\left (2 \, x + 1\right )} \log \left (2\right ) - x\right )} \log \left (-x + \log \left (5\right )\right ) - 2 \, x\right )}}{x^{2} \log \left (3\right ) - x^{2} \log \left (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. 94 vs.
\(2 (24) = 48\).
time = 0.31, size = 94, normalized size = 3.24 \begin {gather*} \frac {\left (- 16 x \log {\left (2 \right )} - 8 x + 16 x \log {\left (3 \right )} - 8 \log {\left (2 \right )} + 8 \log {\left (3 \right )}\right ) \log {\left (- x + \log {\left (5 \right )} \right )}}{- x^{2} \log {\left (3 \right )} + x^{2} \log {\left (2 \right )}} - \frac {x \left (- 16 \log {\left (2 \right )} - 8 + 16 \log {\left (3 \right )}\right ) - 4 \log {\left (2 \right )} + 4 \log {\left (3 \right )}}{x^{2} \left (- \log {\left (3 \right )} + \log {\left (2 \right )}\right )} + \frac {4 \log {\left (- x + \log {\left (5 \right )} \right )}^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 262 vs.
\(2 (30) = 60\).
time = 0.39, size = 262, normalized size = 9.03 \begin {gather*} -\frac {8 \, {\left (2 \, {\left (x - \log \left (5\right )\right )} \log \left (3\right ) + 2 \, \log \left (5\right ) \log \left (3\right ) - 2 \, {\left (x - \log \left (5\right )\right )} \log \left (2\right ) - 2 \, \log \left (5\right ) \log \left (2\right ) - x + \log \left (3\right ) - \log \left (2\right )\right )} \log \left (-x + \log \left (5\right )\right )}{{\left (x - \log \left (5\right )\right )}^{2} \log \left (3\right ) + 2 \, {\left (x - \log \left (5\right )\right )} \log \left (5\right ) \log \left (3\right ) + \log \left (5\right )^{2} \log \left (3\right ) - {\left (x - \log \left (5\right )\right )}^{2} \log \left (2\right ) - 2 \, {\left (x - \log \left (5\right )\right )} \log \left (5\right ) \log \left (2\right ) - \log \left (5\right )^{2} \log \left (2\right )} + \frac {4 \, \log \left (-x + \log \left (5\right )\right )^{2}}{{\left (x - \log \left (5\right )\right )}^{2} + 2 \, {\left (x - \log \left (5\right )\right )} \log \left (5\right ) + \log \left (5\right )^{2}} + \frac {4 \, {\left (4 \, {\left (x - \log \left (5\right )\right )} \log \left (3\right ) + 4 \, \log \left (5\right ) \log \left (3\right ) - 4 \, {\left (x - \log \left (5\right )\right )} \log \left (2\right ) - 4 \, \log \left (5\right ) \log \left (2\right ) - 2 \, x + \log \left (3\right ) - \log \left (2\right )\right )}}{{\left (x - \log \left (5\right )\right )}^{2} \log \left (3\right ) + 2 \, {\left (x - \log \left (5\right )\right )} \log \left (5\right ) \log \left (3\right ) + \log \left (5\right )^{2} \log \left (3\right ) - {\left (x - \log \left (5\right )\right )}^{2} \log \left (2\right ) - 2 \, {\left (x - \log \left (5\right )\right )} \log \left (5\right ) \log \left (2\right ) - \log \left (5\right )^{2} \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\ln \left (5\right )\,\left (8\,x+\ln \left (2\right )\,\left (16\,x+8\right )-\ln \left (3\right )\,\left (16\,x+8\right )\right )-\ln \left (2\right )\,\left (32\,x^2+16\,x\right )+\ln \left (3\right )\,\left (32\,x^2+16\,x\right )+{\ln \left (\ln \left (5\right )-x\right )}^2\,\left (8\,x\,\ln \left (3\right )-8\,x\,\ln \left (2\right )+\ln \left (5\right )\,\left (8\,\ln \left (2\right )-8\,\ln \left (3\right )\right )\right )-\ln \left (\ln \left (5\right )-x\right )\,\left (\ln \left (5\right )\,\left (8\,x+\ln \left (2\right )\,\left (16\,x+16\right )-\ln \left (3\right )\,\left (16\,x+16\right )\right )-\ln \left (2\right )\,\left (16\,x^2+24\,x\right )+\ln \left (3\right )\,\left (16\,x^2+24\,x\right )-8\,x^2\right )-16\,x^2}{\ln \left (5\right )\,\left (x^3\,\ln \left (2\right )-x^3\,\ln \left (3\right )\right )-x^4\,\ln \left (2\right )+x^4\,\ln \left (3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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