Optimal. Leaf size=28 \[ \frac {1}{9} \log ^2(2) \left (-5+2 x^2-(2-4 x \log (5))^4\right )^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(195\) vs. \(2(28)=56\).
time = 0.05, antiderivative size = 195, normalized size of antiderivative = 6.96, number of steps
used = 7, number of rules used = 1, integrand size = 143, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.007, Rules used = {12}
\begin {gather*} \frac {65536}{9} x^8 \log ^2(2) \log ^8(5)-\frac {262144}{9} x^7 \log ^2(2) \log ^7(5)+\frac {458752}{9} x^6 \log ^2(2) \log ^6(5)-\frac {1024}{9} x^6 \log ^2(2) \log ^4(5)-\frac {458752}{9} x^5 \log ^2(2) \log ^5(5)+\frac {2048}{9} x^5 \log ^2(2) \log ^3(5)-\frac {512}{3} x^4 \log ^2(2) \log ^2(5)+\frac {4}{9} x^4 \log ^2(2)+\frac {289280}{9} x^4 \log ^2(2) \log ^4(5)+\frac {512}{9} x^3 \log ^2(2) \log (5)-13312 x^3 \log ^2(2) \log ^3(5)+\frac {32512}{9} x^2 \log ^2(2) \log ^2(5)-\frac {28}{3} x^2 \log ^2(2)-\frac {1792}{3} x \log ^2(2) \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \left (\left (-168 x+16 x^3\right ) \log ^2(2)+\left (-5376+1536 x^2\right ) \log ^2(2) \log (5)+\left (65024 x-6144 x^3\right ) \log ^2(2) \log ^2(5)+\left (-359424 x^2+10240 x^4\right ) \log ^2(2) \log ^3(5)+\left (1157120 x^3-6144 x^5\right ) \log ^2(2) \log ^4(5)-2293760 x^4 \log ^2(2) \log ^5(5)+2752512 x^5 \log ^2(2) \log ^6(5)-1835008 x^6 \log ^2(2) \log ^7(5)+524288 x^7 \log ^2(2) \log ^8(5)\right ) \, dx\\ &=-\frac {458752}{9} x^5 \log ^2(2) \log ^5(5)+\frac {458752}{9} x^6 \log ^2(2) \log ^6(5)-\frac {262144}{9} x^7 \log ^2(2) \log ^7(5)+\frac {65536}{9} x^8 \log ^2(2) \log ^8(5)+\frac {1}{9} \log ^2(2) \int \left (-168 x+16 x^3\right ) \, dx+\frac {1}{9} \left (\log ^2(2) \log (5)\right ) \int \left (-5376+1536 x^2\right ) \, dx+\frac {1}{9} \left (\log ^2(2) \log ^2(5)\right ) \int \left (65024 x-6144 x^3\right ) \, dx+\frac {1}{9} \left (\log ^2(2) \log ^3(5)\right ) \int \left (-359424 x^2+10240 x^4\right ) \, dx+\frac {1}{9} \left (\log ^2(2) \log ^4(5)\right ) \int \left (1157120 x^3-6144 x^5\right ) \, dx\\ &=-\frac {28}{3} x^2 \log ^2(2)+\frac {4}{9} x^4 \log ^2(2)-\frac {1792}{3} x \log ^2(2) \log (5)+\frac {512}{9} x^3 \log ^2(2) \log (5)+\frac {32512}{9} x^2 \log ^2(2) \log ^2(5)-\frac {512}{3} x^4 \log ^2(2) \log ^2(5)-13312 x^3 \log ^2(2) \log ^3(5)+\frac {2048}{9} x^5 \log ^2(2) \log ^3(5)+\frac {289280}{9} x^4 \log ^2(2) \log ^4(5)-\frac {1024}{9} x^6 \log ^2(2) \log ^4(5)-\frac {458752}{9} x^5 \log ^2(2) \log ^5(5)+\frac {458752}{9} x^6 \log ^2(2) \log ^6(5)-\frac {262144}{9} x^7 \log ^2(2) \log ^7(5)+\frac {65536}{9} x^8 \log ^2(2) \log ^8(5)\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(118\) vs. \(2(28)=56\).
time = 0.02, size = 118, normalized size = 4.21 \begin {gather*} \frac {8}{9} \log ^2(2) \left (-\frac {21 x^2}{2}-672 x \log (5)+4064 x^2 \log ^2(5)-32768 x^7 \log ^7(5)+8192 x^8 \log ^8(5)-256 x^5 \log ^3(5) \left (-1+224 \log ^2(5)\right )-64 x^3 \log (5) \left (-1+234 \log ^2(5)\right )+128 x^6 \log ^4(5) \left (-1+448 \log ^2(5)\right )+\frac {1}{2} x^4 \left (1-384 \log ^2(5)+72320 \log ^4(5)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.33, size = 48, normalized size = 1.71
method | result | size |
default | \(\frac {\ln \left (2\right )^{2} \left (256 x^{4} \ln \left (5\right )^{4}-512 x^{3} \ln \left (5\right )^{3}+384 x^{2} \ln \left (5\right )^{2}-128 x \ln \left (5\right )-2 x^{2}+21\right )^{2}}{9}\) | \(48\) |
gosper | \(\frac {4 \ln \left (2\right )^{2} x \left (16384 x^{7} \ln \left (5\right )^{8}-65536 x^{6} \ln \left (5\right )^{7}+114688 x^{5} \ln \left (5\right )^{6}-114688 x^{4} \ln \left (5\right )^{5}-256 \ln \left (5\right )^{4} x^{5}+72320 x^{3} \ln \left (5\right )^{4}+512 x^{4} \ln \left (5\right )^{3}-29952 x^{2} \ln \left (5\right )^{3}-384 x^{3} \ln \left (5\right )^{2}+8128 x \ln \left (5\right )^{2}+128 x^{2} \ln \left (5\right )+x^{3}-1344 \ln \left (5\right )-21 x \right )}{9}\) | \(114\) |
norman | \(\left (\frac {32512 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{9}-\frac {28 \ln \left (2\right )^{2}}{3}\right ) x^{2}+\left (-13312 \ln \left (2\right )^{2} \ln \left (5\right )^{3}+\frac {512 \ln \left (2\right )^{2} \ln \left (5\right )}{9}\right ) x^{3}+\left (-\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{5}}{9}+\frac {2048 \ln \left (2\right )^{2} \ln \left (5\right )^{3}}{9}\right ) x^{5}+\left (\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{6}}{9}-\frac {1024 \ln \left (2\right )^{2} \ln \left (5\right )^{4}}{9}\right ) x^{6}+\left (\frac {289280 \ln \left (2\right )^{2} \ln \left (5\right )^{4}}{9}-\frac {512 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{3}+\frac {4 \ln \left (2\right )^{2}}{9}\right ) x^{4}-\frac {1792 x \ln \left (2\right )^{2} \ln \left (5\right )}{3}-\frac {262144 \ln \left (2\right )^{2} \ln \left (5\right )^{7} x^{7}}{9}+\frac {65536 \ln \left (2\right )^{2} \ln \left (5\right )^{8} x^{8}}{9}\) | \(162\) |
risch | \(\frac {65536 \ln \left (2\right )^{2} \ln \left (5\right )^{8} x^{8}}{9}-\frac {262144 \ln \left (2\right )^{2} \ln \left (5\right )^{7} x^{7}}{9}+\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{6} x^{6}}{9}-\frac {458752 \ln \left (2\right )^{2} \ln \left (5\right )^{5} x^{5}}{9}-\frac {1024 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{6}}{9}+\frac {289280 \ln \left (2\right )^{2} \ln \left (5\right )^{4} x^{4}}{9}+\frac {2048 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{5}}{9}-13312 \ln \left (2\right )^{2} \ln \left (5\right )^{3} x^{3}-\frac {512 \ln \left (2\right )^{2} \ln \left (5\right )^{2} x^{4}}{3}+\frac {32512 x^{2} \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{9}-\frac {516128 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{27}+\frac {512 \ln \left (2\right )^{2} \ln \left (5\right ) x^{3}}{9}-\frac {1792 x \ln \left (2\right )^{2} \ln \left (5\right )}{3}+\frac {4 x^{4} \ln \left (2\right )^{2}}{9}-\frac {28 x^{2} \ln \left (2\right )^{2}}{3}+49 \ln \left (2\right )^{2}\) | \(186\) |
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. 148 vs.
\(2 (26) = 52\).
time = 0.26, size = 148, normalized size = 5.29 \begin {gather*} \frac {65536}{9} \, x^{8} \log \left (5\right )^{8} \log \left (2\right )^{2} - \frac {262144}{9} \, x^{7} \log \left (5\right )^{7} \log \left (2\right )^{2} + \frac {458752}{9} \, x^{6} \log \left (5\right )^{6} \log \left (2\right )^{2} - \frac {458752}{9} \, x^{5} \log \left (5\right )^{5} \log \left (2\right )^{2} - \frac {512}{9} \, {\left (2 \, x^{6} - 565 \, x^{4}\right )} \log \left (5\right )^{4} \log \left (2\right )^{2} + \frac {1024}{9} \, {\left (2 \, x^{5} - 117 \, x^{3}\right )} \log \left (5\right )^{3} \log \left (2\right )^{2} - \frac {256}{9} \, {\left (6 \, x^{4} - 127 \, x^{2}\right )} \log \left (5\right )^{2} \log \left (2\right )^{2} + \frac {256}{9} \, {\left (2 \, x^{3} - 21 \, x\right )} \log \left (5\right ) \log \left (2\right )^{2} + \frac {4}{9} \, {\left (x^{4} - 21 \, x^{2}\right )} \log \left (2\right )^{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. 148 vs.
\(2 (26) = 52\).
time = 0.36, size = 148, normalized size = 5.29 \begin {gather*} \frac {65536}{9} \, x^{8} \log \left (5\right )^{8} \log \left (2\right )^{2} - \frac {262144}{9} \, x^{7} \log \left (5\right )^{7} \log \left (2\right )^{2} + \frac {458752}{9} \, x^{6} \log \left (5\right )^{6} \log \left (2\right )^{2} - \frac {458752}{9} \, x^{5} \log \left (5\right )^{5} \log \left (2\right )^{2} - \frac {512}{9} \, {\left (2 \, x^{6} - 565 \, x^{4}\right )} \log \left (5\right )^{4} \log \left (2\right )^{2} + \frac {1024}{9} \, {\left (2 \, x^{5} - 117 \, x^{3}\right )} \log \left (5\right )^{3} \log \left (2\right )^{2} - \frac {256}{9} \, {\left (6 \, x^{4} - 127 \, x^{2}\right )} \log \left (5\right )^{2} \log \left (2\right )^{2} + \frac {256}{9} \, {\left (2 \, x^{3} - 21 \, x\right )} \log \left (5\right ) \log \left (2\right )^{2} + \frac {4}{9} \, {\left (x^{4} - 21 \, x^{2}\right )} \log \left (2\right )^{2} \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. 199 vs.
\(2 (24) = 48\).
time = 0.03, size = 199, normalized size = 7.11 \begin {gather*} \frac {65536 x^{8} \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{8}}{9} - \frac {262144 x^{7} \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{7}}{9} + x^{6} \left (- \frac {1024 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{4}}{9} + \frac {458752 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{6}}{9}\right ) + x^{5} \left (- \frac {458752 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{5}}{9} + \frac {2048 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{3}}{9}\right ) + x^{4} \left (- \frac {512 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{2}}{3} + \frac {4 \log {\left (2 \right )}^{2}}{9} + \frac {289280 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{4}}{9}\right ) + x^{3} \left (- 13312 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{3} + \frac {512 \log {\left (2 \right )}^{2} \log {\left (5 \right )}}{9}\right ) + x^{2} \left (- \frac {28 \log {\left (2 \right )}^{2}}{3} + \frac {32512 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{2}}{9}\right ) - \frac {1792 x \log {\left (2 \right )}^{2} \log {\left (5 \right )}}{3} \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. 148 vs.
\(2 (26) = 52\).
time = 0.40, size = 148, normalized size = 5.29 \begin {gather*} \frac {65536}{9} \, x^{8} \log \left (5\right )^{8} \log \left (2\right )^{2} - \frac {262144}{9} \, x^{7} \log \left (5\right )^{7} \log \left (2\right )^{2} + \frac {458752}{9} \, x^{6} \log \left (5\right )^{6} \log \left (2\right )^{2} - \frac {458752}{9} \, x^{5} \log \left (5\right )^{5} \log \left (2\right )^{2} - \frac {512}{9} \, {\left (2 \, x^{6} - 565 \, x^{4}\right )} \log \left (5\right )^{4} \log \left (2\right )^{2} + \frac {1024}{9} \, {\left (2 \, x^{5} - 117 \, x^{3}\right )} \log \left (5\right )^{3} \log \left (2\right )^{2} - \frac {256}{9} \, {\left (6 \, x^{4} - 127 \, x^{2}\right )} \log \left (5\right )^{2} \log \left (2\right )^{2} + \frac {256}{9} \, {\left (2 \, x^{3} - 21 \, x\right )} \log \left (5\right ) \log \left (2\right )^{2} + \frac {4}{9} \, {\left (x^{4} - 21 \, x^{2}\right )} \log \left (2\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 163, normalized size = 5.82 \begin {gather*} \frac {65536\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^8\,x^8}{9}-\frac {262144\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^7\,x^7}{9}+\left (\frac {458752\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^6}{9}-\frac {1024\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^4}{9}\right )\,x^6+\left (\frac {2048\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^3}{9}-\frac {458752\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^5}{9}\right )\,x^5+\left (\frac {4\,{\ln \left (2\right )}^2}{9}-\frac {512\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^2}{3}+\frac {289280\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^4}{9}\right )\,x^4+\left (\frac {512\,{\ln \left (2\right )}^2\,\ln \left (5\right )}{9}-13312\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^3\right )\,x^3+\left (\frac {32512\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^2}{9}-\frac {28\,{\ln \left (2\right )}^2}{3}\right )\,x^2-\frac {1792\,{\ln \left (2\right )}^2\,\ln \left (5\right )\,x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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