Integrand size = 613, antiderivative size = 35 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\frac {\log \left (x^2\right ) \left (5+\log \left (5+x \left (-x+\frac {x}{x+\log (x)}\right )\right )\right )}{e^x-x^2} \]
[Out]
Timed out. \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\text {\$Aborted} \]
[In]
[Out]
Rubi steps Aborted
Time = 1.31 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.31 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\frac {\log \left (x^2\right ) \left (5+\log \left (\frac {x \left (5+x-x^2\right )-\left (-5+x^2\right ) \log (x)}{x+\log (x)}\right )\right )}{e^x-x^2} \]
[In]
[Out]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.20 (sec) , antiderivative size = 1449, normalized size of antiderivative = 41.40
\[\text {Expression too large to display}\]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.40 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (\log \left (x\right ) \log \left (-\frac {x^{3} - x^{2} + {\left (x^{2} - 5\right )} \log \left (x\right ) - 5 \, x}{x + \log \left (x\right )}\right ) + 5 \, \log \left (x\right )\right )}}{x^{2} - e^{x}} \]
[In]
[Out]
Time = 0.80 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.17 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\frac {2 \log {\left (x \right )} \log {\left (\frac {- x^{3} + x^{2} + 5 x + \left (5 - x^{2}\right ) \log {\left (x \right )}}{x + \log {\left (x \right )}} \right )} + 10 \log {\left (x \right )}}{- x^{2} + e^{x}} \]
[In]
[Out]
none
Time = 0.46 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.46 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (\log \left (-x^{3} + x^{2} - {\left (x^{2} - 5\right )} \log \left (x\right ) + 5 \, x\right ) \log \left (x\right ) - \log \left (x + \log \left (x\right )\right ) \log \left (x\right ) + 5 \, \log \left (x\right )\right )}}{x^{2} - e^{x}} \]
[In]
[Out]
none
Time = 1.48 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.51 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (\log \left (-x^{3} - x^{2} \log \left (x\right ) + x^{2} + 5 \, x + 5 \, \log \left (x\right )\right ) \log \left (x\right ) - \log \left (x + \log \left (x\right )\right ) \log \left (x\right ) + 5 \, \log \left (x\right )\right )}}{x^{2} - e^{x}} \]
[In]
[Out]
Time = 12.71 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.37 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\frac {\ln \left (x^2\right )\,\left (\ln \left (\frac {5\,x+5\,\ln \left (x\right )-x^2\,\ln \left (x\right )+x^2-x^3}{x+\ln \left (x\right )}\right )+5\right )}{{\mathrm {e}}^x-x^2} \]
[In]
[Out]