Integrand size = 383, antiderivative size = 28 \[ \int \frac {-200 x-1592 x^2+96 x^3+256 x^4+e^3 \left (-40 x-320 x^2\right )+\left (2000+400 e^3-80 x-320 x^2\right ) \log (x)+\left (-40 x-320 x^2\right ) \log ^2(x)+400 \log ^3(x)}{381924 x+625 e^{12} x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 \left (12500 x-500 x^2-2000 x^3\right )+e^6 \left (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5\right )+e^3 \left (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7\right )+\left (309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 \left (37500 x-1500 x^2-6000 x^3\right )+e^3 \left (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5\right )\right ) \log ^2(x)+\left (93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 \left (37500 x-1500 x^2-6000 x^3\right )\right ) \log ^4(x)+\left (12500 x+2500 e^3 x-500 x^2-2000 x^3\right ) \log ^6(x)+625 x \log ^8(x)} \, dx=\frac {4}{7-\left (x+4 x^2-5 \left (5+e^3+\log ^2(x)\right )\right )^2} \]
Leaf count is larger than twice the leaf count of optimal. \(69\) vs. \(2(28)=56\).
Time = 0.08 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.46 \[ \int \frac {-200 x-1592 x^2+96 x^3+256 x^4+e^3 \left (-40 x-320 x^2\right )+\left (2000+400 e^3-80 x-320 x^2\right ) \log (x)+\left (-40 x-320 x^2\right ) \log ^2(x)+400 \log ^3(x)}{381924 x+625 e^{12} x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 \left (12500 x-500 x^2-2000 x^3\right )+e^6 \left (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5\right )+e^3 \left (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7\right )+\left (309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 \left (37500 x-1500 x^2-6000 x^3\right )+e^3 \left (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5\right )\right ) \log ^2(x)+\left (93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 \left (37500 x-1500 x^2-6000 x^3\right )\right ) \log ^4(x)+\left (12500 x+2500 e^3 x-500 x^2-2000 x^3\right ) \log ^6(x)+625 x \log ^8(x)} \, dx=-\frac {4}{618+25 e^6-50 x-199 x^2+8 x^3+16 x^4-10 e^3 \left (-25+x+4 x^2\right )+10 \left (25+5 e^3-x-4 x^2\right ) \log ^2(x)+25 \log ^4(x)} \]
Integrate[(-200*x - 1592*x^2 + 96*x^3 + 256*x^4 + E^3*(-40*x - 320*x^2) + (2000 + 400*E^3 - 80*x - 320*x^2)*Log[x] + (-40*x - 320*x^2)*Log[x]^2 + 40 0*Log[x]^3)/(381924*x + 625*E^12*x - 61800*x^2 - 243464*x^3 + 29788*x^4 + 58577*x^5 - 4784*x^6 - 6304*x^7 + 256*x^8 + 256*x^9 + E^9*(12500*x - 500*x ^2 - 2000*x^3) + E^6*(93400*x - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5 ) + E^3*(309000*x - 37360*x^2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 960*x ^6 - 1280*x^7) + (309000*x + 2500*E^9*x - 37360*x^2 - 147940*x^3 + 11980*x ^4 + 23760*x^5 - 960*x^6 - 1280*x^7 + E^6*(37500*x - 1500*x^2 - 6000*x^3) + E^3*(186800*x - 15000*x^2 - 59700*x^3 + 2400*x^4 + 4800*x^5))*Log[x]^2 + (93400*x + 3750*E^6*x - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5 + E^3* (37500*x - 1500*x^2 - 6000*x^3))*Log[x]^4 + (12500*x + 2500*E^3*x - 500*x^ 2 - 2000*x^3)*Log[x]^6 + 625*x*Log[x]^8),x]
-4/(618 + 25*E^6 - 50*x - 199*x^2 + 8*x^3 + 16*x^4 - 10*E^3*(-25 + x + 4*x ^2) + 10*(25 + 5*E^3 - x - 4*x^2)*Log[x]^2 + 25*Log[x]^4)
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.
| \(\displaystyle \int \frac {256 x^4+96 x^3-1592 x^2+e^3 \left (-320 x^2-40 x\right )+\left (-320 x^2-40 x\right ) \log ^2(x)+\left (-320 x^2-80 x+400 e^3+2000\right ) \log (x)-200 x+400 \log ^3(x)}{256 x^9+256 x^8-6304 x^7-4784 x^6+58577 x^5+29788 x^4-243464 x^3-61800 x^2+e^9 \left (-2000 x^3-500 x^2+12500 x\right )+\left (-2000 x^3-500 x^2+2500 e^3 x+12500 x\right ) \log ^6(x)+e^6 \left (2400 x^5+1200 x^4-29850 x^3-7500 x^2+93400 x\right )+\left (2400 x^5+1200 x^4-29850 x^3-7500 x^2+e^3 \left (-6000 x^3-1500 x^2+37500 x\right )+3750 e^6 x+93400 x\right ) \log ^4(x)+e^3 \left (-1280 x^7-960 x^6+23760 x^5+11980 x^4-147940 x^3-37360 x^2+309000 x\right )+\left (-1280 x^7-960 x^6+23760 x^5+11980 x^4-147940 x^3-37360 x^2+e^6 \left (-6000 x^3-1500 x^2+37500 x\right )+e^3 \left (4800 x^5+2400 x^4-59700 x^3-15000 x^2+186800 x\right )+2500 e^9 x+309000 x\right ) \log ^2(x)+625 e^{12} x+381924 x+625 x \log ^8(x)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {256 x^4+96 x^3-1592 x^2+e^3 \left (-320 x^2-40 x\right )+\left (-320 x^2-40 x\right ) \log ^2(x)+\left (-320 x^2-80 x+400 e^3+2000\right ) \log (x)-200 x+400 \log ^3(x)}{256 x^9+256 x^8-6304 x^7-4784 x^6+58577 x^5+29788 x^4-243464 x^3-61800 x^2+e^9 \left (-2000 x^3-500 x^2+12500 x\right )+\left (-2000 x^3-500 x^2+2500 e^3 x+12500 x\right ) \log ^6(x)+e^6 \left (2400 x^5+1200 x^4-29850 x^3-7500 x^2+93400 x\right )+\left (2400 x^5+1200 x^4-29850 x^3-7500 x^2+e^3 \left (-6000 x^3-1500 x^2+37500 x\right )+3750 e^6 x+93400 x\right ) \log ^4(x)+e^3 \left (-1280 x^7-960 x^6+23760 x^5+11980 x^4-147940 x^3-37360 x^2+309000 x\right )+\left (-1280 x^7-960 x^6+23760 x^5+11980 x^4-147940 x^3-37360 x^2+e^6 \left (-6000 x^3-1500 x^2+37500 x\right )+e^3 \left (4800 x^5+2400 x^4-59700 x^3-15000 x^2+186800 x\right )+2500 e^9 x+309000 x\right ) \log ^2(x)+\left (381924+625 e^{12}\right ) x+625 x \log ^8(x)}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (8 x^2+x-10 \log (x)\right ) \left (4 x^2+x-5 \log ^2(x)-25 \left (1+\frac {e^3}{5}\right )\right )}{x \left (16 x^4+8 x^3-199 x^2-10 e^3 \left (4 x^2+x-25\right )+10 \left (-4 x^2-x+5 e^3+25\right ) \log ^2(x)-50 x+25 \log ^4(x)+618 \left (1+\frac {25 e^6}{618}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 8 \int -\frac {\left (8 x^2+x-10 \log (x)\right ) \left (-4 x^2-x+5 \log ^2(x)+5 \left (5+e^3\right )\right )}{x \left (16 x^4+8 x^3-199 x^2-50 x+25 \log ^4(x)+10 \left (-4 x^2-x+5 \left (5+e^3\right )\right ) \log ^2(x)+10 e^3 \left (-4 x^2-x+25\right )+25 e^6+618\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -8 \int \frac {\left (8 x^2+x-10 \log (x)\right ) \left (-4 x^2-x+5 \log ^2(x)+5 \left (5+e^3\right )\right )}{x \left (16 x^4+8 x^3-199 x^2-50 x+25 \log ^4(x)+10 \left (-4 x^2-x+5 \left (5+e^3\right )\right ) \log ^2(x)+10 e^3 \left (-4 x^2-x+25\right )+25 e^6+618\right )^2}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle -8 \int \frac {\left (8 x^2+x-10 \log (x)\right ) \left (-4 x^2-x+5 \log ^2(x)+5 \left (5+e^3\right )\right )}{x \left (16 x^4+8 x^3-199 x^2-50 x+25 \log ^4(x)+10 \left (-4 x^2-x+5 \left (5+e^3\right )\right ) \log ^2(x)+10 e^3 \left (-4 x^2-x+25\right )+618 \left (1+\frac {25 e^6}{618}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -8 \int \left (-\frac {32 x^3}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}-\frac {12 x^2}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}+\frac {40 \log ^2(x) x}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}+\frac {40 \log (x) x}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}-\frac {\left (1-40 \left (5+e^3\right )\right ) x}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}+\frac {5 \log ^2(x)}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}+\frac {10 \log (x)}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}+\frac {5 \left (5+e^3\right )}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}-\frac {50 \log ^3(x)}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2 x}+\frac {50 \left (-5-e^3\right ) \log (x)}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2 x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -8 \left (5 \left (5+e^3\right ) \int \frac {1}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx+\left (199+40 e^3\right ) \int \frac {x}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx-12 \int \frac {x^2}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx-32 \int \frac {x^3}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx+10 \int \frac {\log (x)}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx-50 \left (5+e^3\right ) \int \frac {\log (x)}{x \left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx+40 \int \frac {x \log (x)}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx+5 \int \frac {\log ^2(x)}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx+40 \int \frac {x \log ^2(x)}{\left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx-50 \int \frac {\log ^3(x)}{x \left (16 x^4+8 x^3-40 \log ^2(x) x^2-199 \left (1+\frac {40 e^3}{199}\right ) x^2-10 \log ^2(x) x-50 \left (1+\frac {e^3}{5}\right ) x+25 \log ^4(x)+250 \left (1+\frac {e^3}{5}\right ) \log ^2(x)+618 \left (1+\frac {25}{618} e^3 \left (10+e^3\right )\right )\right )^2}dx\right )\) |
Int[(-200*x - 1592*x^2 + 96*x^3 + 256*x^4 + E^3*(-40*x - 320*x^2) + (2000 + 400*E^3 - 80*x - 320*x^2)*Log[x] + (-40*x - 320*x^2)*Log[x]^2 + 400*Log[ x]^3)/(381924*x + 625*E^12*x - 61800*x^2 - 243464*x^3 + 29788*x^4 + 58577* x^5 - 4784*x^6 - 6304*x^7 + 256*x^8 + 256*x^9 + E^9*(12500*x - 500*x^2 - 2 000*x^3) + E^6*(93400*x - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5) + E^ 3*(309000*x - 37360*x^2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 960*x^6 - 1 280*x^7) + (309000*x + 2500*E^9*x - 37360*x^2 - 147940*x^3 + 11980*x^4 + 2 3760*x^5 - 960*x^6 - 1280*x^7 + E^6*(37500*x - 1500*x^2 - 6000*x^3) + E^3* (186800*x - 15000*x^2 - 59700*x^3 + 2400*x^4 + 4800*x^5))*Log[x]^2 + (9340 0*x + 3750*E^6*x - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5 + E^3*(37500 *x - 1500*x^2 - 6000*x^3))*Log[x]^4 + (12500*x + 2500*E^3*x - 500*x^2 - 20 00*x^3)*Log[x]^6 + 625*x*Log[x]^8),x]
3.4.56.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(80\) vs. \(2(28)=56\).
Time = 0.70 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.89
| method | result | size |
| risch | \(-\frac {4}{25 \ln \left (x \right )^{4}-40 x^{2} \ln \left (x \right )^{2}+16 x^{4}+50 \,{\mathrm e}^{3} \ln \left (x \right )^{2}-10 x \ln \left (x \right )^{2}-40 x^{2} {\mathrm e}^{3}+8 x^{3}+250 \ln \left (x \right )^{2}+25 \,{\mathrm e}^{6}-10 x \,{\mathrm e}^{3}-199 x^{2}+250 \,{\mathrm e}^{3}-50 x +618}\) | \(81\) |
| parallelrisch | \(-\frac {4}{25 \ln \left (x \right )^{4}-40 x^{2} \ln \left (x \right )^{2}+16 x^{4}+50 \,{\mathrm e}^{3} \ln \left (x \right )^{2}-10 x \ln \left (x \right )^{2}-40 x^{2} {\mathrm e}^{3}+8 x^{3}+250 \ln \left (x \right )^{2}+25 \,{\mathrm e}^{6}-10 x \,{\mathrm e}^{3}-199 x^{2}+250 \,{\mathrm e}^{3}-50 x +618}\) | \(83\) |
| default | \(-\frac {4}{16 x^{4}-40 x^{2} \ln \left (x \right )^{2}+25 \ln \left (x \right )^{4}+8 x^{3}-40 \,{\mathrm e}^{2 \ln \left (x \right )+3}-10 x \ln \left (x \right )^{2}+50 \,{\mathrm e}^{3} \ln \left (x \right )^{2}-199 x^{2}-10 \,{\mathrm e}^{3+\ln \left (x \right )}+25 \,{\mathrm e}^{6}+250 \ln \left (x \right )^{2}-50 x +250 \,{\mathrm e}^{3}+618}\) | \(85\) |
int((400*ln(x)^3+(-320*x^2-40*x)*ln(x)^2+(400*exp(3)-320*x^2-80*x+2000)*ln (x)+(-320*x^2-40*x)*exp(3)+256*x^4+96*x^3-1592*x^2-200*x)/(625*x*ln(x)^8+( 2500*x*exp(3)-2000*x^3-500*x^2+12500*x)*ln(x)^6+(3750*x*exp(3)^2+(-6000*x^ 3-1500*x^2+37500*x)*exp(3)+2400*x^5+1200*x^4-29850*x^3-7500*x^2+93400*x)*l n(x)^4+(2500*x*exp(3)^3+(-6000*x^3-1500*x^2+37500*x)*exp(3)^2+(4800*x^5+24 00*x^4-59700*x^3-15000*x^2+186800*x)*exp(3)-1280*x^7-960*x^6+23760*x^5+119 80*x^4-147940*x^3-37360*x^2+309000*x)*ln(x)^2+625*x*exp(3)^4+(-2000*x^3-50 0*x^2+12500*x)*exp(3)^3+(2400*x^5+1200*x^4-29850*x^3-7500*x^2+93400*x)*exp (3)^2+(-1280*x^7-960*x^6+23760*x^5+11980*x^4-147940*x^3-37360*x^2+309000*x )*exp(3)+256*x^9+256*x^8-6304*x^7-4784*x^6+58577*x^5+29788*x^4-243464*x^3- 61800*x^2+381924*x),x,method=_RETURNVERBOSE)
-4/(25*ln(x)^4-40*x^2*ln(x)^2+16*x^4+50*exp(3)*ln(x)^2-10*x*ln(x)^2-40*x^2 *exp(3)+8*x^3+250*ln(x)^2+25*exp(6)-10*x*exp(3)-199*x^2+250*exp(3)-50*x+61 8)
Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (26) = 52\).
Time = 0.25 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.29 \[ \int \frac {-200 x-1592 x^2+96 x^3+256 x^4+e^3 \left (-40 x-320 x^2\right )+\left (2000+400 e^3-80 x-320 x^2\right ) \log (x)+\left (-40 x-320 x^2\right ) \log ^2(x)+400 \log ^3(x)}{381924 x+625 e^{12} x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 \left (12500 x-500 x^2-2000 x^3\right )+e^6 \left (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5\right )+e^3 \left (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7\right )+\left (309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 \left (37500 x-1500 x^2-6000 x^3\right )+e^3 \left (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5\right )\right ) \log ^2(x)+\left (93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 \left (37500 x-1500 x^2-6000 x^3\right )\right ) \log ^4(x)+\left (12500 x+2500 e^3 x-500 x^2-2000 x^3\right ) \log ^6(x)+625 x \log ^8(x)} \, dx=-\frac {4}{16 \, x^{4} + 25 \, \log \left (x\right )^{4} + 8 \, x^{3} - 10 \, {\left (4 \, x^{2} + x - 5 \, e^{3} - 25\right )} \log \left (x\right )^{2} - 199 \, x^{2} - 10 \, {\left (4 \, x^{2} + x - 25\right )} e^{3} - 50 \, x + 25 \, e^{6} + 618} \]
integrate((400*log(x)^3+(-320*x^2-40*x)*log(x)^2+(400*exp(3)-320*x^2-80*x+ 2000)*log(x)+(-320*x^2-40*x)*exp(3)+256*x^4+96*x^3-1592*x^2-200*x)/(625*x* log(x)^8+(2500*x*exp(3)-2000*x^3-500*x^2+12500*x)*log(x)^6+(3750*x*exp(3)^ 2+(-6000*x^3-1500*x^2+37500*x)*exp(3)+2400*x^5+1200*x^4-29850*x^3-7500*x^2 +93400*x)*log(x)^4+(2500*x*exp(3)^3+(-6000*x^3-1500*x^2+37500*x)*exp(3)^2+ (4800*x^5+2400*x^4-59700*x^3-15000*x^2+186800*x)*exp(3)-1280*x^7-960*x^6+2 3760*x^5+11980*x^4-147940*x^3-37360*x^2+309000*x)*log(x)^2+625*x*exp(3)^4+ (-2000*x^3-500*x^2+12500*x)*exp(3)^3+(2400*x^5+1200*x^4-29850*x^3-7500*x^2 +93400*x)*exp(3)^2+(-1280*x^7-960*x^6+23760*x^5+11980*x^4-147940*x^3-37360 *x^2+309000*x)*exp(3)+256*x^9+256*x^8-6304*x^7-4784*x^6+58577*x^5+29788*x^ 4-243464*x^3-61800*x^2+381924*x),x, algorithm=\
-4/(16*x^4 + 25*log(x)^4 + 8*x^3 - 10*(4*x^2 + x - 5*e^3 - 25)*log(x)^2 - 199*x^2 - 10*(4*x^2 + x - 25)*e^3 - 50*x + 25*e^6 + 618)
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (24) = 48\).
Time = 0.27 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.68 \[ \int \frac {-200 x-1592 x^2+96 x^3+256 x^4+e^3 \left (-40 x-320 x^2\right )+\left (2000+400 e^3-80 x-320 x^2\right ) \log (x)+\left (-40 x-320 x^2\right ) \log ^2(x)+400 \log ^3(x)}{381924 x+625 e^{12} x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 \left (12500 x-500 x^2-2000 x^3\right )+e^6 \left (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5\right )+e^3 \left (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7\right )+\left (309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 \left (37500 x-1500 x^2-6000 x^3\right )+e^3 \left (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5\right )\right ) \log ^2(x)+\left (93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 \left (37500 x-1500 x^2-6000 x^3\right )\right ) \log ^4(x)+\left (12500 x+2500 e^3 x-500 x^2-2000 x^3\right ) \log ^6(x)+625 x \log ^8(x)} \, dx=- \frac {4}{16 x^{4} + 8 x^{3} - 40 x^{2} e^{3} - 199 x^{2} - 10 x e^{3} - 50 x + \left (- 40 x^{2} - 10 x + 250 + 50 e^{3}\right ) \log {\left (x \right )}^{2} + 25 \log {\left (x \right )}^{4} + 618 + 250 e^{3} + 25 e^{6}} \]
integrate((400*ln(x)**3+(-320*x**2-40*x)*ln(x)**2+(400*exp(3)-320*x**2-80* x+2000)*ln(x)+(-320*x**2-40*x)*exp(3)+256*x**4+96*x**3-1592*x**2-200*x)/(6 25*x*ln(x)**8+(2500*x*exp(3)-2000*x**3-500*x**2+12500*x)*ln(x)**6+(3750*x* exp(3)**2+(-6000*x**3-1500*x**2+37500*x)*exp(3)+2400*x**5+1200*x**4-29850* x**3-7500*x**2+93400*x)*ln(x)**4+(2500*x*exp(3)**3+(-6000*x**3-1500*x**2+3 7500*x)*exp(3)**2+(4800*x**5+2400*x**4-59700*x**3-15000*x**2+186800*x)*exp (3)-1280*x**7-960*x**6+23760*x**5+11980*x**4-147940*x**3-37360*x**2+309000 *x)*ln(x)**2+625*x*exp(3)**4+(-2000*x**3-500*x**2+12500*x)*exp(3)**3+(2400 *x**5+1200*x**4-29850*x**3-7500*x**2+93400*x)*exp(3)**2+(-1280*x**7-960*x* *6+23760*x**5+11980*x**4-147940*x**3-37360*x**2+309000*x)*exp(3)+256*x**9+ 256*x**8-6304*x**7-4784*x**6+58577*x**5+29788*x**4-243464*x**3-61800*x**2+ 381924*x),x)
-4/(16*x**4 + 8*x**3 - 40*x**2*exp(3) - 199*x**2 - 10*x*exp(3) - 50*x + (- 40*x**2 - 10*x + 250 + 50*exp(3))*log(x)**2 + 25*log(x)**4 + 618 + 250*exp (3) + 25*exp(6))
Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (26) = 52\).
Time = 0.29 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.36 \[ \int \frac {-200 x-1592 x^2+96 x^3+256 x^4+e^3 \left (-40 x-320 x^2\right )+\left (2000+400 e^3-80 x-320 x^2\right ) \log (x)+\left (-40 x-320 x^2\right ) \log ^2(x)+400 \log ^3(x)}{381924 x+625 e^{12} x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 \left (12500 x-500 x^2-2000 x^3\right )+e^6 \left (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5\right )+e^3 \left (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7\right )+\left (309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 \left (37500 x-1500 x^2-6000 x^3\right )+e^3 \left (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5\right )\right ) \log ^2(x)+\left (93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 \left (37500 x-1500 x^2-6000 x^3\right )\right ) \log ^4(x)+\left (12500 x+2500 e^3 x-500 x^2-2000 x^3\right ) \log ^6(x)+625 x \log ^8(x)} \, dx=-\frac {4}{16 \, x^{4} + 25 \, \log \left (x\right )^{4} + 8 \, x^{3} - x^{2} {\left (40 \, e^{3} + 199\right )} - 10 \, {\left (4 \, x^{2} + x - 5 \, e^{3} - 25\right )} \log \left (x\right )^{2} - 10 \, x {\left (e^{3} + 5\right )} + 25 \, e^{6} + 250 \, e^{3} + 618} \]
integrate((400*log(x)^3+(-320*x^2-40*x)*log(x)^2+(400*exp(3)-320*x^2-80*x+ 2000)*log(x)+(-320*x^2-40*x)*exp(3)+256*x^4+96*x^3-1592*x^2-200*x)/(625*x* log(x)^8+(2500*x*exp(3)-2000*x^3-500*x^2+12500*x)*log(x)^6+(3750*x*exp(3)^ 2+(-6000*x^3-1500*x^2+37500*x)*exp(3)+2400*x^5+1200*x^4-29850*x^3-7500*x^2 +93400*x)*log(x)^4+(2500*x*exp(3)^3+(-6000*x^3-1500*x^2+37500*x)*exp(3)^2+ (4800*x^5+2400*x^4-59700*x^3-15000*x^2+186800*x)*exp(3)-1280*x^7-960*x^6+2 3760*x^5+11980*x^4-147940*x^3-37360*x^2+309000*x)*log(x)^2+625*x*exp(3)^4+ (-2000*x^3-500*x^2+12500*x)*exp(3)^3+(2400*x^5+1200*x^4-29850*x^3-7500*x^2 +93400*x)*exp(3)^2+(-1280*x^7-960*x^6+23760*x^5+11980*x^4-147940*x^3-37360 *x^2+309000*x)*exp(3)+256*x^9+256*x^8-6304*x^7-4784*x^6+58577*x^5+29788*x^ 4-243464*x^3-61800*x^2+381924*x),x, algorithm=\
-4/(16*x^4 + 25*log(x)^4 + 8*x^3 - x^2*(40*e^3 + 199) - 10*(4*x^2 + x - 5* e^3 - 25)*log(x)^2 - 10*x*(e^3 + 5) + 25*e^6 + 250*e^3 + 618)
Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (26) = 52\).
Time = 63.86 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.86 \[ \int \frac {-200 x-1592 x^2+96 x^3+256 x^4+e^3 \left (-40 x-320 x^2\right )+\left (2000+400 e^3-80 x-320 x^2\right ) \log (x)+\left (-40 x-320 x^2\right ) \log ^2(x)+400 \log ^3(x)}{381924 x+625 e^{12} x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 \left (12500 x-500 x^2-2000 x^3\right )+e^6 \left (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5\right )+e^3 \left (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7\right )+\left (309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 \left (37500 x-1500 x^2-6000 x^3\right )+e^3 \left (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5\right )\right ) \log ^2(x)+\left (93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 \left (37500 x-1500 x^2-6000 x^3\right )\right ) \log ^4(x)+\left (12500 x+2500 e^3 x-500 x^2-2000 x^3\right ) \log ^6(x)+625 x \log ^8(x)} \, dx=-\frac {8}{16 \, x^{4} - 40 \, x^{2} \log \left (x\right )^{2} + 25 \, \log \left (x\right )^{4} + 8 \, x^{3} - 40 \, x^{2} e^{3} - 10 \, x \log \left (x\right )^{2} + 50 \, e^{3} \log \left (x\right )^{2} - 199 \, x^{2} - 10 \, x e^{3} + 250 \, \log \left (x\right )^{2} - 50 \, x + 25 \, e^{6} + 250 \, e^{3} + 618} \]
integrate((400*log(x)^3+(-320*x^2-40*x)*log(x)^2+(400*exp(3)-320*x^2-80*x+ 2000)*log(x)+(-320*x^2-40*x)*exp(3)+256*x^4+96*x^3-1592*x^2-200*x)/(625*x* log(x)^8+(2500*x*exp(3)-2000*x^3-500*x^2+12500*x)*log(x)^6+(3750*x*exp(3)^ 2+(-6000*x^3-1500*x^2+37500*x)*exp(3)+2400*x^5+1200*x^4-29850*x^3-7500*x^2 +93400*x)*log(x)^4+(2500*x*exp(3)^3+(-6000*x^3-1500*x^2+37500*x)*exp(3)^2+ (4800*x^5+2400*x^4-59700*x^3-15000*x^2+186800*x)*exp(3)-1280*x^7-960*x^6+2 3760*x^5+11980*x^4-147940*x^3-37360*x^2+309000*x)*log(x)^2+625*x*exp(3)^4+ (-2000*x^3-500*x^2+12500*x)*exp(3)^3+(2400*x^5+1200*x^4-29850*x^3-7500*x^2 +93400*x)*exp(3)^2+(-1280*x^7-960*x^6+23760*x^5+11980*x^4-147940*x^3-37360 *x^2+309000*x)*exp(3)+256*x^9+256*x^8-6304*x^7-4784*x^6+58577*x^5+29788*x^ 4-243464*x^3-61800*x^2+381924*x),x, algorithm=\
-8/(16*x^4 - 40*x^2*log(x)^2 + 25*log(x)^4 + 8*x^3 - 40*x^2*e^3 - 10*x*log (x)^2 + 50*e^3*log(x)^2 - 199*x^2 - 10*x*e^3 + 250*log(x)^2 - 50*x + 25*e^ 6 + 250*e^3 + 618)
Timed out. \[ \int \frac {-200 x-1592 x^2+96 x^3+256 x^4+e^3 \left (-40 x-320 x^2\right )+\left (2000+400 e^3-80 x-320 x^2\right ) \log (x)+\left (-40 x-320 x^2\right ) \log ^2(x)+400 \log ^3(x)}{381924 x+625 e^{12} x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 \left (12500 x-500 x^2-2000 x^3\right )+e^6 \left (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5\right )+e^3 \left (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7\right )+\left (309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 \left (37500 x-1500 x^2-6000 x^3\right )+e^3 \left (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5\right )\right ) \log ^2(x)+\left (93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 \left (37500 x-1500 x^2-6000 x^3\right )\right ) \log ^4(x)+\left (12500 x+2500 e^3 x-500 x^2-2000 x^3\right ) \log ^6(x)+625 x \log ^8(x)} \, dx=\int -\frac {200\,x+{\ln \left (x\right )}^2\,\left (320\,x^2+40\,x\right )+{\mathrm {e}}^3\,\left (320\,x^2+40\,x\right )-400\,{\ln \left (x\right )}^3+\ln \left (x\right )\,\left (320\,x^2+80\,x-400\,{\mathrm {e}}^3-2000\right )+1592\,x^2-96\,x^3-256\,x^4}{381924\,x+625\,x\,{\ln \left (x\right )}^8+625\,x\,{\mathrm {e}}^{12}-{\mathrm {e}}^3\,\left (1280\,x^7+960\,x^6-23760\,x^5-11980\,x^4+147940\,x^3+37360\,x^2-309000\,x\right )+{\ln \left (x\right )}^4\,\left (93400\,x+3750\,x\,{\mathrm {e}}^6-{\mathrm {e}}^3\,\left (6000\,x^3+1500\,x^2-37500\,x\right )-7500\,x^2-29850\,x^3+1200\,x^4+2400\,x^5\right )-{\mathrm {e}}^9\,\left (2000\,x^3+500\,x^2-12500\,x\right )+{\ln \left (x\right )}^6\,\left (12500\,x+2500\,x\,{\mathrm {e}}^3-500\,x^2-2000\,x^3\right )+{\ln \left (x\right )}^2\,\left (309000\,x+2500\,x\,{\mathrm {e}}^9-{\mathrm {e}}^6\,\left (6000\,x^3+1500\,x^2-37500\,x\right )+{\mathrm {e}}^3\,\left (4800\,x^5+2400\,x^4-59700\,x^3-15000\,x^2+186800\,x\right )-37360\,x^2-147940\,x^3+11980\,x^4+23760\,x^5-960\,x^6-1280\,x^7\right )+{\mathrm {e}}^6\,\left (2400\,x^5+1200\,x^4-29850\,x^3-7500\,x^2+93400\,x\right )-61800\,x^2-243464\,x^3+29788\,x^4+58577\,x^5-4784\,x^6-6304\,x^7+256\,x^8+256\,x^9} \,d x \]
int(-(200*x + log(x)^2*(40*x + 320*x^2) + exp(3)*(40*x + 320*x^2) - 400*lo g(x)^3 + log(x)*(80*x - 400*exp(3) + 320*x^2 - 2000) + 1592*x^2 - 96*x^3 - 256*x^4)/(381924*x + 625*x*log(x)^8 + 625*x*exp(12) - exp(3)*(37360*x^2 - 309000*x + 147940*x^3 - 11980*x^4 - 23760*x^5 + 960*x^6 + 1280*x^7) + log (x)^4*(93400*x + 3750*x*exp(6) - exp(3)*(1500*x^2 - 37500*x + 6000*x^3) - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5) - exp(9)*(500*x^2 - 12500*x + 2000*x^3) + log(x)^6*(12500*x + 2500*x*exp(3) - 500*x^2 - 2000*x^3) + log( x)^2*(309000*x + 2500*x*exp(9) - exp(6)*(1500*x^2 - 37500*x + 6000*x^3) + exp(3)*(186800*x - 15000*x^2 - 59700*x^3 + 2400*x^4 + 4800*x^5) - 37360*x^ 2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 960*x^6 - 1280*x^7) + exp(6)*(934 00*x - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5) - 61800*x^2 - 243464*x^ 3 + 29788*x^4 + 58577*x^5 - 4784*x^6 - 6304*x^7 + 256*x^8 + 256*x^9),x)
int(-(200*x + log(x)^2*(40*x + 320*x^2) + exp(3)*(40*x + 320*x^2) - 400*lo g(x)^3 + log(x)*(80*x - 400*exp(3) + 320*x^2 - 2000) + 1592*x^2 - 96*x^3 - 256*x^4)/(381924*x + 625*x*log(x)^8 + 625*x*exp(12) - exp(3)*(37360*x^2 - 309000*x + 147940*x^3 - 11980*x^4 - 23760*x^5 + 960*x^6 + 1280*x^7) + log (x)^4*(93400*x + 3750*x*exp(6) - exp(3)*(1500*x^2 - 37500*x + 6000*x^3) - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5) - exp(9)*(500*x^2 - 12500*x + 2000*x^3) + log(x)^6*(12500*x + 2500*x*exp(3) - 500*x^2 - 2000*x^3) + log( x)^2*(309000*x + 2500*x*exp(9) - exp(6)*(1500*x^2 - 37500*x + 6000*x^3) + exp(3)*(186800*x - 15000*x^2 - 59700*x^3 + 2400*x^4 + 4800*x^5) - 37360*x^ 2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 960*x^6 - 1280*x^7) + exp(6)*(934 00*x - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5) - 61800*x^2 - 243464*x^ 3 + 29788*x^4 + 58577*x^5 - 4784*x^6 - 6304*x^7 + 256*x^8 + 256*x^9), x)