Integrand size = 234, antiderivative size = 34 \[ \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx=\frac {\left (x-\left (x+\frac {1}{5} \log ^2\left (x^2\right )\right )^2\right )^2}{x \log \left (\frac {6}{5 x^2}\right )} \] Output:
(x-(1/5*ln(x^2)^2+x)^2)^2/x/ln(6/5/x^2)
Leaf count is larger than twice the leaf count of optimal. \(204\) vs. \(2(34)=68\).
Time = 0.08 (sec) , antiderivative size = 204, normalized size of antiderivative = 6.00 \[ \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx=\frac {1}{625} \left (-180 \log ^5\left (\frac {6}{5 x^2}\right )-600 \log ^4\left (\frac {6}{5 x^2}\right ) \left (\log (x)+\log \left (x^2\right )\right )-600 \log ^2\left (\frac {6}{5 x^2}\right ) \log (x) \left (-1+6 \log ^2\left (x^2\right )\right )-100 \log ^3\left (\frac {6}{5 x^2}\right ) \left (-1+24 \log (x) \log \left (x^2\right )+6 \log ^2\left (x^2\right )\right )+\frac {\left (25 (-1+x) x+10 x \log ^2\left (x^2\right )+\log ^4\left (x^2\right )\right )^2}{x \log \left (\frac {6}{5 x^2}\right )}-40 \log ^2\left (x^2\right ) \left (5 \log \left (x^2\right )-3 \log ^3\left (x^2\right )+15 \log (x) \left (-1+\log ^2\left (x^2\right )\right )\right )+300 \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right ) \left (\log (x) \left (4-8 \log ^2\left (x^2\right )\right )+\log \left (x^2\right ) \left (-1+\log ^2\left (x^2\right )\right )\right )\right ) \] Input:
Integrate[(1250*x^2 - 2500*x^3 + 1250*x^4 + (625*x^2 - 2500*x^3 + 1875*x^4 )*Log[6/(5*x^2)] + (-2000*x^2 + 2000*x^3)*Log[6/(5*x^2)]*Log[x^2] + (-1000 *x^2 + 1000*x^3 + (-500*x^2 + 1000*x^3)*Log[6/(5*x^2)])*Log[x^2]^2 + (-400 *x + 1200*x^2)*Log[6/(5*x^2)]*Log[x^2]^3 + (-100*x + 300*x^2 + 150*x^2*Log [6/(5*x^2)])*Log[x^2]^4 + 240*x*Log[6/(5*x^2)]*Log[x^2]^5 + 40*x*Log[x^2]^ 6 + 16*Log[6/(5*x^2)]*Log[x^2]^7 + (2 - Log[6/(5*x^2)])*Log[x^2]^8)/(625*x ^2*Log[6/(5*x^2)]^2),x]
Output:
(-180*Log[6/(5*x^2)]^5 - 600*Log[6/(5*x^2)]^4*(Log[x] + Log[x^2]) - 600*Lo g[6/(5*x^2)]^2*Log[x]*(-1 + 6*Log[x^2]^2) - 100*Log[6/(5*x^2)]^3*(-1 + 24* Log[x]*Log[x^2] + 6*Log[x^2]^2) + (25*(-1 + x)*x + 10*x*Log[x^2]^2 + Log[x ^2]^4)^2/(x*Log[6/(5*x^2)]) - 40*Log[x^2]^2*(5*Log[x^2] - 3*Log[x^2]^3 + 1 5*Log[x]*(-1 + Log[x^2]^2)) + 300*Log[6/(5*x^2)]*Log[x^2]*(Log[x]*(4 - 8*L og[x^2]^2) + Log[x^2]*(-1 + Log[x^2]^2)))/625
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {1250 x^4-2500 x^3+1250 x^2+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+40 x \log ^6\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+\left (300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )-100 x\right ) \log ^4\left (x^2\right )+\left (1200 x^2-400 x\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (1000 x^3-1000 x^2+\left (1000 x^3-500 x^2\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (2000 x^3-2000 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (1875 x^4-2500 x^3+625 x^2\right ) \log \left (\frac {6}{5 x^2}\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{625} \int \frac {\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+40 x \log ^6\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )-50 \left (-3 \log \left (\frac {6}{5 x^2}\right ) x^2-6 x^2+2 x\right ) \log ^4\left (x^2\right )-400 \left (x-3 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )-500 \left (-2 x^3+2 x^2+\left (x^2-2 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )-2000 \left (x^2-x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+1250 x^4-2500 x^3+1250 x^2+625 \left (3 x^4-4 x^3+x^2\right ) \log \left (\frac {6}{5 x^2}\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \frac {\left (\log ^4\left (x^2\right )+10 x \log ^2\left (x^2\right )+25 (x-1) x\right ) \left (\log \left (\frac {6}{5 x^2}\right ) \left (-\log ^4\left (x^2\right )+16 \log ^3\left (x^2\right )+10 x \log ^2\left (x^2\right )+80 x \log \left (x^2\right )+25 x (3 x-1)\right )+2 \left (\log ^4\left (x^2\right )+10 x \log ^2\left (x^2\right )+25 (x-1) x\right )\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (-\frac {\left (\log \left (\frac {6}{5 x^2}\right )-2\right ) \log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {16 \log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )}+\frac {40 \log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {240 \log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}+\frac {50 \left (3 \log \left (\frac {6}{5 x^2}\right ) x+6 x-2\right ) \log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {400 (3 x-1) \log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}+\frac {500 \left (2 \log \left (\frac {6}{5 x^2}\right ) x+2 x-\log \left (\frac {6}{5 x^2}\right )-2\right ) \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}+\frac {2000 (x-1) \log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}+\frac {625 (x-1) \left (3 \log \left (\frac {6}{5 x^2}\right ) x+2 x-\log \left (\frac {6}{5 x^2}\right )-2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{625} \left (-\int \frac {\log ^8\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )}dx+16 \int \frac {\log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )}dx+240 \int \frac {\log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}dx+150 \int \frac {\log ^4\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}dx+1200 \int \frac {\log ^3\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}dx-400 \int \frac {\log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}dx-1000 \int \frac {\log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}dx+1000 \int \frac {x \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}dx-500 \int \frac {\log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}dx+1000 \int \frac {x \log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}dx+2 \int \frac {\log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )}dx+40 \int \frac {\log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}dx+300 \int \frac {\log ^4\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}dx-100 \int \frac {\log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}dx-1200 \log \left (\frac {6}{5 x^2}\right ) \operatorname {ExpIntegralEi}\left (-\log \left (\frac {6}{5 x^2}\right )\right )+200 \sqrt {30} \sqrt {\frac {1}{x^2}} x \log \left (\frac {6}{5 x^2}\right ) \operatorname {ExpIntegralEi}\left (-\frac {1}{2} \log \left (\frac {6}{5 x^2}\right )\right )-1200 \log \left (x^2\right ) \operatorname {ExpIntegralEi}\left (-\log \left (\frac {6}{5 x^2}\right )\right )+200 \sqrt {30} \sqrt {\frac {1}{x^2}} x \log \left (x^2\right ) \operatorname {ExpIntegralEi}\left (-\frac {1}{2} \log \left (\frac {6}{5 x^2}\right )\right )-1000 x^2+\frac {625 x (1-x)^2}{\log \left (\frac {6}{5 x^2}\right )}+2000 x\right )\) |
Input:
Int[(1250*x^2 - 2500*x^3 + 1250*x^4 + (625*x^2 - 2500*x^3 + 1875*x^4)*Log[ 6/(5*x^2)] + (-2000*x^2 + 2000*x^3)*Log[6/(5*x^2)]*Log[x^2] + (-1000*x^2 + 1000*x^3 + (-500*x^2 + 1000*x^3)*Log[6/(5*x^2)])*Log[x^2]^2 + (-400*x + 1 200*x^2)*Log[6/(5*x^2)]*Log[x^2]^3 + (-100*x + 300*x^2 + 150*x^2*Log[6/(5* x^2)])*Log[x^2]^4 + 240*x*Log[6/(5*x^2)]*Log[x^2]^5 + 40*x*Log[x^2]^6 + 16 *Log[6/(5*x^2)]*Log[x^2]^7 + (2 - Log[6/(5*x^2)])*Log[x^2]^8)/(625*x^2*Log [6/(5*x^2)]^2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(88\) vs. \(2(30)=60\).
Time = 296.15 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.62
| method | result | size |
| parallelrisch | \(\frac {8400 x \ln \left (x^{2}\right )^{6}-21000 x \ln \left (x^{2}\right )^{4}-210000 x^{2} \ln \left (x^{2}\right )^{2}+63000 \ln \left (x^{2}\right )^{4} x^{2}+210000 x^{3} \ln \left (x^{2}\right )^{2}+262500 x^{2}-525000 x^{3}+262500 x^{4}+420 \ln \left (x^{2}\right )^{8}}{262500 x \ln \left (\frac {6}{5 x^{2}}\right )}\) | \(89\) |
| risch | \(\text {Expression too large to display}\) | \(35897\) |
Input:
int(1/625*((-ln(6/5/x^2)+2)*ln(x^2)^8+16*ln(6/5/x^2)*ln(x^2)^7+40*x*ln(x^2 )^6+240*x*ln(6/5/x^2)*ln(x^2)^5+(150*x^2*ln(6/5/x^2)+300*x^2-100*x)*ln(x^2 )^4+(1200*x^2-400*x)*ln(6/5/x^2)*ln(x^2)^3+((1000*x^3-500*x^2)*ln(6/5/x^2) +1000*x^3-1000*x^2)*ln(x^2)^2+(2000*x^3-2000*x^2)*ln(6/5/x^2)*ln(x^2)+(187 5*x^4-2500*x^3+625*x^2)*ln(6/5/x^2)+1250*x^4-2500*x^3+1250*x^2)/x^2/ln(6/5 /x^2)^2,x,method=_RETURNVERBOSE)
Output:
1/262500/x*(8400*x*ln(x^2)^6-21000*x*ln(x^2)^4-210000*x^2*ln(x^2)^2+63000* ln(x^2)^4*x^2+210000*x^3*ln(x^2)^2+262500*x^2-525000*x^3+262500*x^4+420*ln (x^2)^8)/ln(6/5/x^2)
Leaf count of result is larger than twice the leaf count of optimal. 285 vs. \(2 (31) = 62\).
Time = 0.10 (sec) , antiderivative size = 285, normalized size of antiderivative = 8.38 \[ \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=\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 )} \] Input:
integrate(1/625*((-log(6/5/x^2)+2)*log(x^2)^8+16*log(6/5/x^2)*log(x^2)^7+4 0*x*log(x^2)^6+240*x*log(6/5/x^2)*log(x^2)^5+(150*x^2*log(6/5/x^2)+300*x^2 -100*x)*log(x^2)^4+(1200*x^2-400*x)*log(6/5/x^2)*log(x^2)^3+((1000*x^3-500 *x^2)*log(6/5/x^2)+1000*x^3-1000*x^2)*log(x^2)^2+(2000*x^3-2000*x^2)*log(6 /5/x^2)*log(x^2)+(1875*x^4-2500*x^3+625*x^2)*log(6/5/x^2)+1250*x^4-2500*x^ 3+1250*x^2)/x^2/log(6/5/x^2)^2,x, algorithm="fricas")
Output:
1/625*(log(6/5)^8 - 8*log(6/5)*log(6/5/x^2)^7 + log(6/5/x^2)^8 + 20*x*log( 6/5)^6 + 4*(7*log(6/5)^2 + 5*x)*log(6/5/x^2)^6 - 8*(7*log(6/5)^3 + 15*x*lo g(6/5))*log(6/5/x^2)^5 + 50*(3*x^2 - x)*log(6/5)^4 + 10*(7*log(6/5)^4 + 30 *x*log(6/5)^2 + 15*x^2 - 5*x)*log(6/5/x^2)^4 + 625*x^4 - 8*(7*log(6/5)^5 + 50*x*log(6/5)^3 + 25*(3*x^2 - x)*log(6/5))*log(6/5/x^2)^3 - 1250*x^3 + 50 0*(x^3 - x^2)*log(6/5)^2 + 4*(7*log(6/5)^6 + 75*x*log(6/5)^4 + 125*x^3 + 7 5*(3*x^2 - x)*log(6/5)^2 - 125*x^2)*log(6/5/x^2)^2 + 625*x^2 - 8*(log(6/5) ^7 + 75*x^2*log(6/5)^3 + 125*(x^3 - x^2)*log(6/5))*log(6/5/x^2))/(x*log(6/ 5/x^2))
Leaf count of result is larger than twice the leaf count of optimal. 1028 vs. \(2 (24) = 48\).
Time = 1.64 (sec) , antiderivative size = 1028, normalized size of antiderivative = 30.24 \[ \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx=\text {Too large to display} \] Input:
integrate(1/625*((-ln(6/5/x**2)+2)*ln(x**2)**8+16*ln(6/5/x**2)*ln(x**2)**7 +40*x*ln(x**2)**6+240*x*ln(6/5/x**2)*ln(x**2)**5+(150*x**2*ln(6/5/x**2)+30 0*x**2-100*x)*ln(x**2)**4+(1200*x**2-400*x)*ln(6/5/x**2)*ln(x**2)**3+((100 0*x**3-500*x**2)*ln(6/5/x**2)+1000*x**3-1000*x**2)*ln(x**2)**2+(2000*x**3- 2000*x**2)*ln(6/5/x**2)*ln(x**2)+(1875*x**4-2500*x**3+625*x**2)*ln(6/5/x** 2)+1250*x**4-2500*x**3+1250*x**2)/x**2/ln(6/5/x**2)**2,x)
Output:
x**2*(-500*log(6) + 500*log(5))/625 + x*(-450*log(5)**2*log(6) - 150*log(6 )**3 - 500*log(5) + 150*log(5)**3 + 500*log(6) + 450*log(5)*log(6)**2)/625 - 4*(-log(6) + log(5))**2*(-4*log(5)*log(6) - 5 + 2*log(5)**2 + 2*log(6)* *2)*log(x)/125 + (-625*x**4 - 500*x**3*log(6)**2 - 500*x**3*log(5)**2 + 12 50*x**3 + 1000*x**3*log(5)*log(6) - 900*x**2*log(5)**2*log(6)**2 - 1000*x* *2*log(5)*log(6) - 150*x**2*log(6)**4 - 150*x**2*log(5)**4 - 625*x**2 + 50 0*x**2*log(5)**2 + 500*x**2*log(6)**2 + 600*x**2*log(5)**3*log(6) + 600*x* *2*log(5)*log(6)**3 - 300*x*log(5)**2*log(6)**4 - 300*x*log(5)**4*log(6)** 2 - 200*x*log(5)*log(6)**3 - 200*x*log(5)**3*log(6) - 20*x*log(6)**6 - 20* x*log(5)**6 + 50*x*log(5)**4 + 50*x*log(6)**4 + 120*x*log(5)**5*log(6) + 3 00*x*log(5)**2*log(6)**2 + 120*x*log(5)*log(6)**5 + 400*x*log(5)**3*log(6) **3 - 70*log(5)**4*log(6)**4 - 28*log(5)**2*log(6)**6 - 28*log(5)**6*log(6 )**2 - log(6)**8 - log(5)**8 + 8*log(5)**7*log(6) + 8*log(5)*log(6)**7 + 5 6*log(5)**5*log(6)**3 + 56*log(5)**3*log(6)**5)/(625*x*log(x**2) - 625*x*l og(6) + 625*x*log(5)) + (-20*x - log(6)**2 - log(5)**2 + 2*log(5)*log(6))* log(x**2)**5/(625*x) + (-20*x*log(6) + 20*x*log(5) - 3*log(5)**2*log(6) - log(6)**3 + log(5)**3 + 3*log(5)*log(6)**2)*log(x**2)**4/(625*x) + (-150*x **2 - 20*x*log(6)**2 - 20*x*log(5)**2 + 50*x + 40*x*log(5)*log(6) - 6*log( 5)**2*log(6)**2 - log(6)**4 - log(5)**4 + 4*log(5)**3*log(6) + 4*log(5)*lo g(6)**3)*log(x**2)**3/(625*x) + (-500*x**3 - 150*x**2*log(6)**2 - 150*x...
Leaf count of result is larger than twice the leaf count of optimal. 627 vs. \(2 (31) = 62\).
Time = 0.17 (sec) , antiderivative size = 627, normalized size of antiderivative = 18.44 \[ \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx=\text {Too large to display} \] Input:
integrate(1/625*((-log(6/5/x^2)+2)*log(x^2)^8+16*log(6/5/x^2)*log(x^2)^7+4 0*x*log(x^2)^6+240*x*log(6/5/x^2)*log(x^2)^5+(150*x^2*log(6/5/x^2)+300*x^2 -100*x)*log(x^2)^4+(1200*x^2-400*x)*log(6/5/x^2)*log(x^2)^3+((1000*x^3-500 *x^2)*log(6/5/x^2)+1000*x^3-1000*x^2)*log(x^2)^2+(2000*x^3-2000*x^2)*log(6 /5/x^2)*log(x^2)+(1875*x^4-2500*x^3+625*x^2)*log(6/5/x^2)+1250*x^4-2500*x^ 3+1250*x^2)/x^2/log(6/5/x^2)^2,x, algorithm="maxima")
Output:
-1/625*(256*log(x)^8 + 1280*x*log(x)^6 + 800*(3*x^2 - x)*log(x)^4 + 625*x^ 4 - 1250*x^3 + 20*(2*log(5)^5 + 10*log(5)*log(3)^4 - 2*log(3)^5 + 10*(log( 5) - log(3))*log(2)^4 - 2*log(2)^5 - 5*(4*log(5)^2 - 1)*log(3)^3 - 5*(4*lo g(5)^2 - 8*log(5)*log(3) + 4*log(3)^2 - 1)*log(2)^3 - 5*log(5)^3 + 5*(4*lo g(5)^3 - 3*log(5))*log(3)^2 + 5*(4*log(5)^3 + 12*log(5)*log(3)^2 - 4*log(3 )^3 - 3*(4*log(5)^2 - 1)*log(3) - 3*log(5))*log(2)^2 - 5*(2*log(5)^4 - 3*l og(5)^2)*log(3) - 5*(2*log(5)^4 - 8*log(5)*log(3)^3 + 2*log(3)^4 + 3*(4*lo g(5)^2 - 1)*log(3)^2 - 3*log(5)^2 - 2*(4*log(5)^3 - 3*log(5))*log(3))*log( 2))*x*log(x) + 2000*(x^3 - x^2)*log(x)^2 + 10*(2*log(5)^6 - 12*log(5)*log( 3)^5 + 2*log(3)^6 - 12*(log(5) - log(3))*log(2)^5 + 2*log(2)^6 + 5*(6*log( 5)^2 - 1)*log(3)^4 + 5*(6*log(5)^2 - 12*log(5)*log(3) + 6*log(3)^2 - 1)*lo g(2)^4 - 5*log(5)^4 - 20*(2*log(5)^3 - log(5))*log(3)^3 - 20*(2*log(5)^3 + 6*log(5)*log(3)^2 - 2*log(3)^3 - (6*log(5)^2 - 1)*log(3) - log(5))*log(2) ^3 + 30*(log(5)^4 - log(5)^2)*log(3)^2 + 30*(log(5)^4 - 4*log(5)*log(3)^3 + log(3)^4 + (6*log(5)^2 - 1)*log(3)^2 - log(5)^2 - 2*(2*log(5)^3 - log(5) )*log(3))*log(2)^2 - 4*(3*log(5)^5 - 5*log(5)^3)*log(3) - 4*(3*log(5)^5 + 15*log(5)*log(3)^4 - 3*log(3)^5 - 5*(6*log(5)^2 - 1)*log(3)^3 - 5*log(5)^3 + 15*(2*log(5)^3 - log(5))*log(3)^2 - 15*(log(5)^4 - log(5)^2)*log(3))*lo g(2))*x + 625*x^2)/(x*(log(5) - log(3) - log(2)) + 2*x*log(x))
\[ \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx=\int { -\frac {{\left (\log \left (\frac {6}{5 \, x^{2}}\right ) - 2\right )} \log \left (x^{2}\right )^{8} - 16 \, \log \left (x^{2}\right )^{7} \log \left (\frac {6}{5 \, x^{2}}\right ) - 40 \, x \log \left (x^{2}\right )^{6} - 240 \, x \log \left (x^{2}\right )^{5} \log \left (\frac {6}{5 \, x^{2}}\right ) - 50 \, {\left (3 \, x^{2} \log \left (\frac {6}{5 \, x^{2}}\right ) + 6 \, x^{2} - 2 \, x\right )} \log \left (x^{2}\right )^{4} - 400 \, {\left (3 \, x^{2} - x\right )} \log \left (x^{2}\right )^{3} \log \left (\frac {6}{5 \, x^{2}}\right ) - 1250 \, x^{4} + 2500 \, x^{3} - 500 \, {\left (2 \, x^{3} - 2 \, x^{2} + {\left (2 \, x^{3} - x^{2}\right )} \log \left (\frac {6}{5 \, x^{2}}\right )\right )} \log \left (x^{2}\right )^{2} - 2000 \, {\left (x^{3} - x^{2}\right )} \log \left (x^{2}\right ) \log \left (\frac {6}{5 \, x^{2}}\right ) - 1250 \, x^{2} - 625 \, {\left (3 \, x^{4} - 4 \, x^{3} + x^{2}\right )} \log \left (\frac {6}{5 \, x^{2}}\right )}{625 \, x^{2} \log \left (\frac {6}{5 \, x^{2}}\right )^{2}} \,d x } \] Input:
integrate(1/625*((-log(6/5/x^2)+2)*log(x^2)^8+16*log(6/5/x^2)*log(x^2)^7+4 0*x*log(x^2)^6+240*x*log(6/5/x^2)*log(x^2)^5+(150*x^2*log(6/5/x^2)+300*x^2 -100*x)*log(x^2)^4+(1200*x^2-400*x)*log(6/5/x^2)*log(x^2)^3+((1000*x^3-500 *x^2)*log(6/5/x^2)+1000*x^3-1000*x^2)*log(x^2)^2+(2000*x^3-2000*x^2)*log(6 /5/x^2)*log(x^2)+(1875*x^4-2500*x^3+625*x^2)*log(6/5/x^2)+1250*x^4-2500*x^ 3+1250*x^2)/x^2/log(6/5/x^2)^2,x, algorithm="giac")
Output:
integrate(-1/625*((log(6/5/x^2) - 2)*log(x^2)^8 - 16*log(x^2)^7*log(6/5/x^ 2) - 40*x*log(x^2)^6 - 240*x*log(x^2)^5*log(6/5/x^2) - 50*(3*x^2*log(6/5/x ^2) + 6*x^2 - 2*x)*log(x^2)^4 - 400*(3*x^2 - x)*log(x^2)^3*log(6/5/x^2) - 1250*x^4 + 2500*x^3 - 500*(2*x^3 - 2*x^2 + (2*x^3 - x^2)*log(6/5/x^2))*log (x^2)^2 - 2000*(x^3 - x^2)*log(x^2)*log(6/5/x^2) - 1250*x^2 - 625*(3*x^4 - 4*x^3 + x^2)*log(6/5/x^2))/(x^2*log(6/5/x^2)^2), x)
Time = 2.74 (sec) , antiderivative size = 520, normalized size of antiderivative = 15.29 \[ \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx =\text {Too large to display} \] Input:
int(((log(6/(5*x^2))*(625*x^2 - 2500*x^3 + 1875*x^4))/625 - (log(x^2)^8*(l og(6/(5*x^2)) - 2))/625 + (log(x^2)^4*(300*x^2 - 100*x + 150*x^2*log(6/(5* x^2))))/625 + (8*x*log(x^2)^6)/125 - (log(x^2)^2*(log(6/(5*x^2))*(500*x^2 - 1000*x^3) + 1000*x^2 - 1000*x^3))/625 + (16*log(x^2)^7*log(6/(5*x^2)))/6 25 + 2*x^2 - 4*x^3 + 2*x^4 - (log(x^2)^3*log(6/(5*x^2))*(400*x - 1200*x^2) )/625 - (log(x^2)*log(6/(5*x^2))*(2000*x^2 - 2000*x^3))/625 + (48*x*log(x^ 2)^5*log(6/(5*x^2)))/125)/(x^2*log(6/(5*x^2))^2),x)
Output:
- ((1000*x^3*log(6/5)^2 - 500*x^2*log(6/5)^3 - 1000*x^2*log(6/5)^2 + 300*x ^2*log(6/5)^4 + 1000*x^3*log(6/5)^3 + 150*x^2*log(6/5)^5 + 625*x^2*log(6/5 ) - 2500*x^3*log(6/5) - 100*x*log(6/5)^4 + 1875*x^4*log(6/5) + 40*x*log(6/ 5)^6 + 2*log(6/5)^8 - log(6/5)^9 + 1250*x^2 - 2500*x^3 + 1250*x^4)/(1250*x ) - (log(x^2)*(1000*x^3*log(6/5)^2 - 500*x^2*log(6/5)^2 + 150*x^2*log(6/5) ^4 - log(6/5)^8 + 625*x^2 - 2500*x^3 + 1875*x^4))/(1250*x))/(log(x^2) - lo g(6/5)) - log(x^2)^2*((182*log(6/5))/125 + ((6*x^2*log(6/5))/25 - x*((192* log(6/5))/125 + (24*log(6/5)^2)/125 + 372/25) + log(6/5)^5/625)/x + (24*lo g(6/5)^2)/125 + (4*log(6/5)^3)/125 + 372/25) - log(x^2)^3*((32*log(6/5))/1 25 + (4*log(6/5)^2)/125 + (log(6/5)^4/625 - x*((32*log(6/5))/125 + 64/25) + (6*x^2)/25)/x + 62/25) - log(x^2)^5*(log(6/5)^2/(625*x) + 4/125) - x*((6 *log(6/5)^3)/25 - (2*log(6/5)^2)/5 - (4*log(6/5))/5 + (3*log(6/5)^4)/25 + 1/2) - x^2*((4*log(6/5))/5 + (4*log(6/5)^2)/5 - 2) - log(x^2)^4*((4*log(6/ 5))/125 - ((8*x)/25 - log(6/5)^3/625)/x + 8/25) - (3*x^3)/2 - log(x^2)^7/( 625*x) - (log(6/5)^7/625 - log(6/5)^8/1250)/x - log(x)*((1456*log(6/5))/12 5 + (172*log(6/5)^2)/125 + (32*log(6/5)^3)/125 + (8*log(6/5)^4)/125 + 2976 /25) - (log(x^2)^6*log(6/5))/(625*x) - (log(x^2)*(x^2*((6*log(6/5)^2)/25 - 4/5) - x*((728*log(6/5))/125 + (96*log(6/5)^2)/125 + (16*log(6/5)^3)/125 + 1488/25) + log(6/5)^6/625 + (4*x^3)/5))/x
Time = 0.19 (sec) , antiderivative size = 86, normalized size of antiderivative = 2.53 \[ \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx=\frac {\mathrm {log}\left (x^{2}\right )^{8}+20 \mathrm {log}\left (x^{2}\right )^{6} x +150 \mathrm {log}\left (x^{2}\right )^{4} x^{2}-50 \mathrm {log}\left (x^{2}\right )^{4} x +500 \mathrm {log}\left (x^{2}\right )^{2} x^{3}-500 \mathrm {log}\left (x^{2}\right )^{2} x^{2}+625 x^{4}-1250 x^{3}+625 x^{2}}{625 \,\mathrm {log}\left (\frac {6}{5 x^{2}}\right ) x} \] Input:
int(1/625*((-log(6/5/x^2)+2)*log(x^2)^8+16*log(6/5/x^2)*log(x^2)^7+40*x*lo g(x^2)^6+240*x*log(6/5/x^2)*log(x^2)^5+(150*x^2*log(6/5/x^2)+300*x^2-100*x )*log(x^2)^4+(1200*x^2-400*x)*log(6/5/x^2)*log(x^2)^3+((1000*x^3-500*x^2)* log(6/5/x^2)+1000*x^3-1000*x^2)*log(x^2)^2+(2000*x^3-2000*x^2)*log(6/5/x^2 )*log(x^2)+(1875*x^4-2500*x^3+625*x^2)*log(6/5/x^2)+1250*x^4-2500*x^3+1250 *x^2)/x^2/log(6/5/x^2)^2,x)
Output:
(log(x**2)**8 + 20*log(x**2)**6*x + 150*log(x**2)**4*x**2 - 50*log(x**2)** 4*x + 500*log(x**2)**2*x**3 - 500*log(x**2)**2*x**2 + 625*x**4 - 1250*x**3 + 625*x**2)/(625*log(6/(5*x**2))*x)