Integrand size = 146, antiderivative size = 28 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=\left (-(1+x)^2+2 x \log \left ((-1+5 (2 x-\log (3)))^2\right )\right )^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(418\) vs. \(2(28)=56\).
Time = 0.56 (sec) , antiderivative size = 418, normalized size of antiderivative = 14.93, number of steps used = 31, number of rules used = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.096, Rules used = {6820, 12, 6874, 45, 2465, 2442, 2436, 2332, 2437, 2338, 2448, 2333, 2342, 2341} \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=x^4+\frac {58 x^3}{15}-4 x^3 \log \left ((-10 x+1+\log (243))^2\right )+\frac {2}{15} x^3 (1+\log (243))-\frac {13 x^2}{5}+\frac {1}{50} x^2 (1+\log (243))^2+\frac {29}{50} x^2 (1+\log (243))-\frac {26 x}{5}+\frac {1}{25} (-10 x+1+\log (243))^2 \log ^2\left ((-10 x+1+\log (243))^2\right )-\frac {2}{25} (1+\log (243)) (-10 x+1+\log (243)) \log ^2\left ((-10 x+1+\log (243))^2\right )+\frac {1}{25} (1+\log (243))^2 \log ^2\left ((-10 x+1+\log (243))^2\right )-\frac {1}{50} x \log (3) (11+\log (243))^2+\frac {1}{250} x (1+\log (243))^3+\frac {29}{250} x (1+\log (243))^2+\frac {147}{25} x (1+\log (243))+\frac {8}{5} x (3-5 \log (9))+\frac {2}{25} (-10 x+1+\log (243))^2-\frac {1}{500} \log (3) (11+\log (243))^3 \log (-10 x+1+\log (243))+\frac {(1+\log (243))^4 \log (-10 x+1+\log (243))}{2500}+\frac {29 (1+\log (243))^3 \log (-10 x+1+\log (243))}{2500}-\frac {13}{250} (1+\log (243))^2 \log (-10 x+1+\log (243))-\frac {13}{25} (1+\log (243)) \log (-10 x+1+\log (243))-\frac {2}{5} \log (-10 x+1+\log (243))-\frac {2}{25} (-10 x+1+\log (243))^2 \log \left ((-10 x+1+\log (243))^2\right )+\frac {8}{25} (1+\log (243)) (-10 x+1+\log (243)) \log \left ((-10 x+1+\log (243))^2\right )+\frac {2}{25} (3-5 \log (9)) (-10 x+1+\log (243)) \log \left ((-10 x+1+\log (243))^2\right )-\frac {1}{10} (x+1)^2 \log (3) (11+\log (243))-\frac {2}{3} (x+1)^3 \log (3) \]
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Rule 12
Rule 45
Rule 2332
Rule 2333
Rule 2338
Rule 2341
Rule 2342
Rule 2436
Rule 2437
Rule 2442
Rule 2448
Rule 2465
Rule 6820
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {4 \left (1+13 x+13 x^2-9 x^3-10 x^4+5 (1+x)^3 \log (3)+\left (-1+30 x^3+x (6-20 \log (3))-5 \log (3)-3 x^2 (1+\log (243))\right ) \log \left ((1-10 x+\log (243))^2\right )+2 x (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )\right )}{1-10 x+\log (243)} \, dx \\ & = 4 \int \frac {1+13 x+13 x^2-9 x^3-10 x^4+5 (1+x)^3 \log (3)+\left (-1+30 x^3+x (6-20 \log (3))-5 \log (3)-3 x^2 (1+\log (243))\right ) \log \left ((1-10 x+\log (243))^2\right )+2 x (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )}{1-10 x+\log (243)} \, dx \\ & = 4 \int \left (-\frac {13 x}{-1+10 x-\log (243)}-\frac {13 x^2}{-1+10 x-\log (243)}+\frac {9 x^3}{-1+10 x-\log (243)}+\frac {10 x^4}{-1+10 x-\log (243)}-\frac {5 (1+x)^3 \log (3)}{-1+10 x-\log (243)}+\frac {1}{1-10 x+\log (243)}+\frac {\left (-1+30 x^3+2 x (3-10 \log (3))-\log (243)-3 x^2 (1+\log (243))\right ) \log \left ((1-10 x+\log (243))^2\right )}{1-10 x+\log (243)}+2 x \log ^2\left ((1-10 x+\log (243))^2\right )\right ) \, dx \\ & = -\frac {2}{5} \log (1-10 x+\log (243))+4 \int \frac {\left (-1+30 x^3+2 x (3-10 \log (3))-\log (243)-3 x^2 (1+\log (243))\right ) \log \left ((1-10 x+\log (243))^2\right )}{1-10 x+\log (243)} \, dx+8 \int x \log ^2\left ((1-10 x+\log (243))^2\right ) \, dx+36 \int \frac {x^3}{-1+10 x-\log (243)} \, dx+40 \int \frac {x^4}{-1+10 x-\log (243)} \, dx-52 \int \frac {x}{-1+10 x-\log (243)} \, dx-52 \int \frac {x^2}{-1+10 x-\log (243)} \, dx-(20 \log (3)) \int \frac {(1+x)^3}{-1+10 x-\log (243)} \, dx \\ & = -\frac {2}{5} \log (1-10 x+\log (243))+4 \int \left (-3 x^2 \log \left ((1-10 x+\log (243))^2\right )+\frac {1}{5} (-3+5 \log (9)) \log \left ((1-10 x+\log (243))^2\right )-\frac {2 (1+\log (243))^2 \log \left ((1-10 x+\log (243))^2\right )}{5 (1-10 x+\log (243))}\right ) \, dx+8 \int \left (\frac {1}{10} (1+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )-\frac {1}{10} (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )\right ) \, dx+36 \int \left (\frac {x^2}{10}+\frac {1}{100} x (1+\log (243))+\frac {(1+\log (243))^2}{1000}+\frac {(1+\log (243))^3}{1000 (-1+10 x-\log (243))}\right ) \, dx+40 \int \left (\frac {x^3}{10}+\frac {1}{100} x^2 (1+\log (243))+\frac {x (1+\log (243))^2}{1000}+\frac {(1+\log (243))^3}{10000}+\frac {(1+\log (243))^4}{10000 (-1+10 x-\log (243))}\right ) \, dx-52 \int \left (\frac {1}{10}+\frac {1+\log (243)}{10 (-1+10 x-\log (243))}\right ) \, dx-52 \int \left (\frac {x}{10}+\frac {1}{100} (1+\log (243))+\frac {(1+\log (243))^2}{100 (-1+10 x-\log (243))}\right ) \, dx-(20 \log (3)) \int \left (\frac {1}{10} (1+x)^2+\frac {1}{100} (1+x) (11+\log (243))+\frac {(11+\log (243))^2}{1000}+\frac {(11+\log (243))^3}{1000 (-1+10 x-\log (243))}\right ) \, dx \\ & = -\frac {26 x}{5}-\frac {13 x^2}{5}+\frac {6 x^3}{5}+x^4-\frac {2}{3} (1+x)^3 \log (3)-\frac {13}{25} x (1+\log (243))+\frac {9}{50} x^2 (1+\log (243))+\frac {2}{15} x^3 (1+\log (243))+\frac {9}{250} x (1+\log (243))^2+\frac {1}{50} x^2 (1+\log (243))^2+\frac {1}{250} x (1+\log (243))^3-\frac {1}{10} (1+x)^2 \log (3) (11+\log (243))-\frac {1}{50} x \log (3) (11+\log (243))^2-\frac {2}{5} \log (1-10 x+\log (243))-\frac {13}{25} (1+\log (243)) \log (1-10 x+\log (243))-\frac {13}{250} (1+\log (243))^2 \log (1-10 x+\log (243))+\frac {9 (1+\log (243))^3 \log (1-10 x+\log (243))}{2500}+\frac {(1+\log (243))^4 \log (1-10 x+\log (243))}{2500}-\frac {1}{500} \log (3) (11+\log (243))^3 \log (1-10 x+\log (243))-\frac {4}{5} \int (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right ) \, dx-12 \int x^2 \log \left ((1-10 x+\log (243))^2\right ) \, dx-\frac {1}{5} (4 (3-5 \log (9))) \int \log \left ((1-10 x+\log (243))^2\right ) \, dx+\frac {1}{5} (4 (1+\log (243))) \int \log ^2\left ((1-10 x+\log (243))^2\right ) \, dx-\frac {1}{5} \left (8 (1+\log (243))^2\right ) \int \frac {\log \left ((1-10 x+\log (243))^2\right )}{1-10 x+\log (243)} \, dx \\ & = -\frac {26 x}{5}-\frac {13 x^2}{5}+\frac {6 x^3}{5}+x^4-\frac {2}{3} (1+x)^3 \log (3)-\frac {13}{25} x (1+\log (243))+\frac {9}{50} x^2 (1+\log (243))+\frac {2}{15} x^3 (1+\log (243))+\frac {9}{250} x (1+\log (243))^2+\frac {1}{50} x^2 (1+\log (243))^2+\frac {1}{250} x (1+\log (243))^3-\frac {1}{10} (1+x)^2 \log (3) (11+\log (243))-\frac {1}{50} x \log (3) (11+\log (243))^2-\frac {2}{5} \log (1-10 x+\log (243))-\frac {13}{25} (1+\log (243)) \log (1-10 x+\log (243))-\frac {13}{250} (1+\log (243))^2 \log (1-10 x+\log (243))+\frac {9 (1+\log (243))^3 \log (1-10 x+\log (243))}{2500}+\frac {(1+\log (243))^4 \log (1-10 x+\log (243))}{2500}-\frac {1}{500} \log (3) (11+\log (243))^3 \log (1-10 x+\log (243))-4 x^3 \log \left ((1-10 x+\log (243))^2\right )+\frac {2}{25} \text {Subst}\left (\int x \log ^2\left (x^2\right ) \, dx,x,1-10 x+\log (243)\right )-80 \int \frac {x^3}{1-10 x+\log (243)} \, dx+\frac {1}{25} (2 (3-5 \log (9))) \text {Subst}\left (\int \log \left (x^2\right ) \, dx,x,1-10 x+\log (243)\right )-\frac {1}{25} (2 (1+\log (243))) \text {Subst}\left (\int \log ^2\left (x^2\right ) \, dx,x,1-10 x+\log (243)\right )+\frac {1}{25} \left (4 (1+\log (243))^2\right ) \text {Subst}\left (\int \frac {\log \left (x^2\right )}{x} \, dx,x,1-10 x+\log (243)\right ) \\ & = -\frac {26 x}{5}-\frac {13 x^2}{5}+\frac {6 x^3}{5}+x^4-\frac {2}{3} (1+x)^3 \log (3)+\frac {8}{5} x (3-5 \log (9))-\frac {13}{25} x (1+\log (243))+\frac {9}{50} x^2 (1+\log (243))+\frac {2}{15} x^3 (1+\log (243))+\frac {9}{250} x (1+\log (243))^2+\frac {1}{50} x^2 (1+\log (243))^2+\frac {1}{250} x (1+\log (243))^3-\frac {1}{10} (1+x)^2 \log (3) (11+\log (243))-\frac {1}{50} x \log (3) (11+\log (243))^2-\frac {2}{5} \log (1-10 x+\log (243))-\frac {13}{25} (1+\log (243)) \log (1-10 x+\log (243))-\frac {13}{250} (1+\log (243))^2 \log (1-10 x+\log (243))+\frac {9 (1+\log (243))^3 \log (1-10 x+\log (243))}{2500}+\frac {(1+\log (243))^4 \log (1-10 x+\log (243))}{2500}-\frac {1}{500} \log (3) (11+\log (243))^3 \log (1-10 x+\log (243))-4 x^3 \log \left ((1-10 x+\log (243))^2\right )+\frac {2}{25} (3-5 \log (9)) (1-10 x+\log (243)) \log \left ((1-10 x+\log (243))^2\right )+\frac {1}{25} (1+\log (243))^2 \log ^2\left ((1-10 x+\log (243))^2\right )-\frac {2}{25} (1+\log (243)) (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )+\frac {1}{25} (1-10 x+\log (243))^2 \log ^2\left ((1-10 x+\log (243))^2\right )-\frac {4}{25} \text {Subst}\left (\int x \log \left (x^2\right ) \, dx,x,1-10 x+\log (243)\right )-80 \int \left (-\frac {x^2}{10}-\frac {1}{100} x (1+\log (243))-\frac {(1+\log (243))^2}{1000}-\frac {(1+\log (243))^3}{1000 (-1+10 x-\log (243))}\right ) \, dx+\frac {1}{25} (8 (1+\log (243))) \text {Subst}\left (\int \log \left (x^2\right ) \, dx,x,1-10 x+\log (243)\right ) \\ & = -\frac {26 x}{5}-\frac {13 x^2}{5}+\frac {58 x^3}{15}+x^4-\frac {2}{3} (1+x)^3 \log (3)+\frac {8}{5} x (3-5 \log (9))+\frac {147}{25} x (1+\log (243))+\frac {29}{50} x^2 (1+\log (243))+\frac {2}{15} x^3 (1+\log (243))+\frac {29}{250} x (1+\log (243))^2+\frac {1}{50} x^2 (1+\log (243))^2+\frac {1}{250} x (1+\log (243))^3-\frac {1}{10} (1+x)^2 \log (3) (11+\log (243))-\frac {1}{50} x \log (3) (11+\log (243))^2+\frac {2}{25} (1-10 x+\log (243))^2-\frac {2}{5} \log (1-10 x+\log (243))-\frac {13}{25} (1+\log (243)) \log (1-10 x+\log (243))-\frac {13}{250} (1+\log (243))^2 \log (1-10 x+\log (243))+\frac {29 (1+\log (243))^3 \log (1-10 x+\log (243))}{2500}+\frac {(1+\log (243))^4 \log (1-10 x+\log (243))}{2500}-\frac {1}{500} \log (3) (11+\log (243))^3 \log (1-10 x+\log (243))-4 x^3 \log \left ((1-10 x+\log (243))^2\right )+\frac {2}{25} (3-5 \log (9)) (1-10 x+\log (243)) \log \left ((1-10 x+\log (243))^2\right )+\frac {8}{25} (1+\log (243)) (1-10 x+\log (243)) \log \left ((1-10 x+\log (243))^2\right )-\frac {2}{25} (1-10 x+\log (243))^2 \log \left ((1-10 x+\log (243))^2\right )+\frac {1}{25} (1+\log (243))^2 \log ^2\left ((1-10 x+\log (243))^2\right )-\frac {2}{25} (1+\log (243)) (1-10 x+\log (243)) \log ^2\left ((1-10 x+\log (243))^2\right )+\frac {1}{25} (1-10 x+\log (243))^2 \log ^2\left ((1-10 x+\log (243))^2\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(72\) vs. \(2(28)=56\).
Time = 0.09 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.57 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=\frac {1}{250} x \left (1000+1500 x+1000 x^2+250 x^3-5655 \log (3)+1131 \log (243)-160 \log (3) \log (243)+32 \log ^2(243)-1000 (1+x)^2 \log \left ((1-10 x+\log (243))^2\right )+1000 x \log ^2\left ((1-10 x+\log (243))^2\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(78\) vs. \(2(25)=50\).
Time = 0.58 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.82
method | result | size |
risch | \(4 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}+\left (-4 x^{3}-8 x^{2}-4 x \right ) \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+\left (1+x \right )^{4}\) | \(79\) |
norman | \(x^{4}+4 x +6 x^{2}+4 x^{3}-4 x \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )-8 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+4 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}-4 x^{3} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )\) | \(138\) |
parallelrisch | \(x^{4}-4 x^{3} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+4 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}+4 x^{3}-8 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )-\frac {3 \ln \left (3\right )^{2}}{2}+\frac {37}{50}+6 x^{2}-4 x \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+\frac {17 \ln \left (3\right )}{5}+4 x\) | \(149\) |
parts | \(-4 \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right ) x^{3}-\frac {12 x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )}{5}+\left (-\ln \left (3\right )^{2}-\frac {2 \ln \left (3\right )}{5}-\frac {1}{25}\right ) \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}+\left (6 \ln \left (3\right )^{2}+\frac {12 \ln \left (3\right )}{5}+\frac {6}{25}\right ) \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )-\frac {4 x}{5}-8 x \ln \left (3\right )+x^{4}+4 x^{3}+6 x^{2}+80 \left (\frac {\ln \left (3\right )^{3}}{80}+\frac {3 \ln \left (3\right )^{2}}{400}+\frac {3 \ln \left (3\right )}{2000}+\frac {1}{10000}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+48 \left (\frac {\ln \left (3\right )}{20}+\frac {1}{100}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+8 \left (x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )-2 x -20 \left (\frac {\ln \left (3\right )}{20}+\frac {1}{100}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )\right ) \ln \left (3\right )-\frac {4 \left (\frac {\ln \left (10 x -5 \ln \left (3\right )-1\right ) \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )}{10}-\frac {\ln \left (10 x -5 \ln \left (3\right )-1\right )^{2}}{10}\right ) \left (-50 \ln \left (3\right )^{2}-20 \ln \left (3\right )-2\right )}{5}+4 \left (-\frac {\ln \left (3\right )^{3}}{4}-\frac {23 \ln \left (3\right )^{2}}{20}-\frac {143 \ln \left (3\right )}{100}-\frac {121}{500}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+\left (24 \ln \left (3\right )+\frac {24}{5}\right ) x -8 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )+4 x^{2} \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )^{2}+\left (-8 \ln \left (3\right )-\frac {8}{5}\right ) x \ln \left (25 \ln \left (3\right )^{2}+\left (-100 x +10\right ) \ln \left (3\right )+100 x^{2}-20 x +1\right )\) | \(463\) |
default | \(\left (-8 \ln \left (3\right )-\frac {8}{5}\right ) x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )+4 \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )^{2} x^{2}-4 \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right ) x^{3}-8 \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right ) x^{2}-\frac {12 x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )}{5}-\frac {4 x}{5}-8 x \ln \left (3\right )+x^{4}+4 x^{3}+6 x^{2}+\left (-\ln \left (3\right )^{2}-\frac {2 \ln \left (3\right )}{5}-\frac {1}{25}\right ) \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )^{2}+\left (6 \ln \left (3\right )^{2}+\frac {12 \ln \left (3\right )}{5}+\frac {6}{25}\right ) \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )+80 \left (\frac {\ln \left (3\right )^{3}}{80}+\frac {3 \ln \left (3\right )^{2}}{400}+\frac {3 \ln \left (3\right )}{2000}+\frac {1}{10000}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+48 \left (\frac {\ln \left (3\right )}{20}+\frac {1}{100}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+8 \left (x \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )-2 x -20 \left (\frac {\ln \left (3\right )}{20}+\frac {1}{100}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )\right ) \ln \left (3\right )-\frac {4 \left (\frac {\ln \left (10 x -5 \ln \left (3\right )-1\right ) \ln \left (25 \ln \left (3\right )^{2}-100 x \ln \left (3\right )+100 x^{2}+10 \ln \left (3\right )-20 x +1\right )}{10}-\frac {\ln \left (10 x -5 \ln \left (3\right )-1\right )^{2}}{10}\right ) \left (-50 \ln \left (3\right )^{2}-20 \ln \left (3\right )-2\right )}{5}+4 \left (-\frac {\ln \left (3\right )^{3}}{4}-\frac {23 \ln \left (3\right )^{2}}{20}-\frac {143 \ln \left (3\right )}{100}-\frac {121}{500}\right ) \ln \left (10 x -5 \ln \left (3\right )-1\right )+\left (24 \ln \left (3\right )+\frac {24}{5}\right ) x\) | \(468\) |
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Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (23) = 46\).
Time = 0.25 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.14 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=x^{4} + 4 \, x^{2} \log \left (100 \, x^{2} - 10 \, {\left (10 \, x - 1\right )} \log \left (3\right ) + 25 \, \log \left (3\right )^{2} - 20 \, x + 1\right )^{2} + 4 \, x^{3} + 6 \, x^{2} - 4 \, {\left (x^{3} + 2 \, x^{2} + x\right )} \log \left (100 \, x^{2} - 10 \, {\left (10 \, x - 1\right )} \log \left (3\right ) + 25 \, \log \left (3\right )^{2} - 20 \, x + 1\right ) + 4 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (22) = 44\).
Time = 0.14 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.29 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=x^{4} + 4 x^{3} + 4 x^{2} \log {\left (100 x^{2} - 20 x + \left (10 - 100 x\right ) \log {\left (3 \right )} + 1 + 25 \log {\left (3 \right )}^{2} \right )}^{2} + 6 x^{2} + 4 x + \left (- 4 x^{3} - 8 x^{2} - 4 x\right ) \log {\left (100 x^{2} - 20 x + \left (10 - 100 x\right ) \log {\left (3 \right )} + 1 + 25 \log {\left (3 \right )}^{2} \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1507 vs. \(2 (23) = 46\).
Time = 0.31 (sec) , antiderivative size = 1507, normalized size of antiderivative = 53.82 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=\text {Too large to display} \]
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Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (23) = 46\).
Time = 0.54 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.14 \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=x^{4} + 4 \, x^{2} \log \left (100 \, x^{2} - 100 \, x \log \left (3\right ) + 25 \, \log \left (3\right )^{2} - 20 \, x + 10 \, \log \left (3\right ) + 1\right )^{2} + 4 \, x^{3} + 6 \, x^{2} - 4 \, {\left (x^{3} + 2 \, x^{2} + x\right )} \log \left (100 \, x^{2} - 100 \, x \log \left (3\right ) + 25 \, \log \left (3\right )^{2} - 20 \, x + 10 \, \log \left (3\right ) + 1\right ) + 4 \, x \]
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Timed out. \[ \int \frac {4+52 x+52 x^2-36 x^3-40 x^4+\left (20+60 x+60 x^2+20 x^3\right ) \log (3)+\left (-4+24 x-12 x^2+120 x^3+\left (-20-80 x-60 x^2\right ) \log (3)\right ) \log \left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )+\left (8 x-80 x^2+40 x \log (3)\right ) \log ^2\left (1-20 x+100 x^2+(10-100 x) \log (3)+25 \log ^2(3)\right )}{1-10 x+5 \log (3)} \, dx=\int \frac {52\,x-\ln \left (25\,{\ln \left (3\right )}^2-\ln \left (3\right )\,\left (100\,x-10\right )-20\,x+100\,x^2+1\right )\,\left (\ln \left (3\right )\,\left (60\,x^2+80\,x+20\right )-24\,x+12\,x^2-120\,x^3+4\right )+\ln \left (3\right )\,\left (20\,x^3+60\,x^2+60\,x+20\right )+{\ln \left (25\,{\ln \left (3\right )}^2-\ln \left (3\right )\,\left (100\,x-10\right )-20\,x+100\,x^2+1\right )}^2\,\left (8\,x+40\,x\,\ln \left (3\right )-80\,x^2\right )+52\,x^2-36\,x^3-40\,x^4+4}{5\,\ln \left (3\right )-10\,x+1} \,d x \]
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