Integrand size = 617, antiderivative size = 29 \[ \int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+\left (-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9\right ) \log (2)+\left (-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9\right ) \log ^2(2)+e^{3 x} \left (25+100 x^3+\left (10+40 x^3\right ) \log (2)+\left (1+4 x^3\right ) \log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+\left (-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5\right ) \log (2)+\left (-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5\right ) \log ^2(2)\right )+e^x \left (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+\left (5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7\right ) \log (2)+\left (507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7\right ) \log ^2(2)\right )}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+\left (-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6\right ) \log (2)+\left (-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6\right ) \log ^2(2)+e^{3 x} \left (25+10 \log (2)+\log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2+\left (-390-150 x-30 x^2\right ) \log (2)+\left (-39-15 x-3 x^2\right ) \log ^2(2)\right )+e^x \left (12675+9750 x+3825 x^2+750 x^3+75 x^4+\left (5070+3900 x+1530 x^2+300 x^3+30 x^4\right ) \log (2)+\left (507+390 x+153 x^2+30 x^3+3 x^4\right ) \log ^2(2)\right )} \, dx=x+x^4-\frac {x}{\left (-4+e^x+x-(3+x)^2\right )^2 (5+\log (2))^2} \] Output:
x-x/(ln(2)+5)^2/(x-(3+x)^2+exp(x)-4)^2+x^4
Time = 0.14 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+\left (-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9\right ) \log (2)+\left (-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9\right ) \log ^2(2)+e^{3 x} \left (25+100 x^3+\left (10+40 x^3\right ) \log (2)+\left (1+4 x^3\right ) \log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+\left (-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5\right ) \log (2)+\left (-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5\right ) \log ^2(2)\right )+e^x \left (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+\left (5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7\right ) \log (2)+\left (507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7\right ) \log ^2(2)\right )}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+\left (-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6\right ) \log (2)+\left (-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6\right ) \log ^2(2)+e^{3 x} \left (25+10 \log (2)+\log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2+\left (-390-150 x-30 x^2\right ) \log (2)+\left (-39-15 x-3 x^2\right ) \log ^2(2)\right )+e^x \left (12675+9750 x+3825 x^2+750 x^3+75 x^4+\left (5070+3900 x+1530 x^2+300 x^3+30 x^4\right ) \log (2)+\left (507+390 x+153 x^2+30 x^3+3 x^4\right ) \log ^2(2)\right )} \, dx=-\frac {\frac {x}{\left (-13+e^x-5 x-x^2\right )^2}-x (5+\log (2))^2-x^4 (5+\log (2))^2}{(5+\log (2))^2} \] Input:
Integrate[(-54912 - 63380*x - 37053*x^2 - 232575*x^3 - 256350*x^4 - 148575 *x^5 - 51525*x^6 - 11400*x^7 - 1500*x^8 - 100*x^9 + (-21970 - 25350*x - 14 820*x^2 - 93030*x^3 - 102540*x^4 - 59430*x^5 - 20610*x^6 - 4560*x^7 - 600* x^8 - 40*x^9)*Log[2] + (-2197 - 2535*x - 1482*x^2 - 9303*x^3 - 10254*x^4 - 5943*x^5 - 2061*x^6 - 456*x^7 - 60*x^8 - 4*x^9)*Log[2]^2 + E^(3*x)*(25 + 100*x^3 + (10 + 40*x^3)*Log[2] + (1 + 4*x^3)*Log[2]^2) + E^(2*x)*(-975 - 3 75*x - 75*x^2 - 3900*x^3 - 1500*x^4 - 300*x^5 + (-390 - 150*x - 30*x^2 - 1 560*x^3 - 600*x^4 - 120*x^5)*Log[2] + (-39 - 15*x - 3*x^2 - 156*x^3 - 60*x ^4 - 12*x^5)*Log[2]^2) + E^x*(12674 + 9752*x + 3825*x^2 + 51450*x^3 + 3907 5*x^4 + 15300*x^5 + 3000*x^6 + 300*x^7 + (5070 + 3900*x + 1530*x^2 + 20580 *x^3 + 15630*x^4 + 6120*x^5 + 1200*x^6 + 120*x^7)*Log[2] + (507 + 390*x + 153*x^2 + 2058*x^3 + 1563*x^4 + 612*x^5 + 120*x^6 + 12*x^7)*Log[2]^2))/(-5 4925 - 63375*x - 37050*x^2 - 12875*x^3 - 2850*x^4 - 375*x^5 - 25*x^6 + (-2 1970 - 25350*x - 14820*x^2 - 5150*x^3 - 1140*x^4 - 150*x^5 - 10*x^6)*Log[2 ] + (-2197 - 2535*x - 1482*x^2 - 515*x^3 - 114*x^4 - 15*x^5 - x^6)*Log[2]^ 2 + E^(3*x)*(25 + 10*Log[2] + Log[2]^2) + E^(2*x)*(-975 - 375*x - 75*x^2 + (-390 - 150*x - 30*x^2)*Log[2] + (-39 - 15*x - 3*x^2)*Log[2]^2) + E^x*(12 675 + 9750*x + 3825*x^2 + 750*x^3 + 75*x^4 + (5070 + 3900*x + 1530*x^2 + 3 00*x^3 + 30*x^4)*Log[2] + (507 + 390*x + 153*x^2 + 30*x^3 + 3*x^4)*Log[2]^ 2)),x]
Output:
-((x/(-13 + E^x - 5*x - x^2)^2 - x*(5 + Log[2])^2 - x^4*(5 + Log[2])^2)/(5 + Log[2])^2)
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.
| \(\displaystyle \int \frac {-100 x^9-1500 x^8-11400 x^7-51525 x^6-148575 x^5-256350 x^4-232575 x^3+e^{3 x} \left (100 x^3+\left (4 x^3+1\right ) \log ^2(2)+\left (40 x^3+10\right ) \log (2)+25\right )-37053 x^2+e^{2 x} \left (-300 x^5-1500 x^4-3900 x^3-75 x^2+\left (-12 x^5-60 x^4-156 x^3-3 x^2-15 x-39\right ) \log ^2(2)+\left (-120 x^5-600 x^4-1560 x^3-30 x^2-150 x-390\right ) \log (2)-375 x-975\right )+e^x \left (300 x^7+3000 x^6+15300 x^5+39075 x^4+51450 x^3+3825 x^2+\left (12 x^7+120 x^6+612 x^5+1563 x^4+2058 x^3+153 x^2+390 x+507\right ) \log ^2(2)+\left (120 x^7+1200 x^6+6120 x^5+15630 x^4+20580 x^3+1530 x^2+3900 x+5070\right ) \log (2)+9752 x+12674\right )+\left (-4 x^9-60 x^8-456 x^7-2061 x^6-5943 x^5-10254 x^4-9303 x^3-1482 x^2-2535 x-2197\right ) \log ^2(2)+\left (-40 x^9-600 x^8-4560 x^7-20610 x^6-59430 x^5-102540 x^4-93030 x^3-14820 x^2-25350 x-21970\right ) \log (2)-63380 x-54912}{-25 x^6-375 x^5-2850 x^4-12875 x^3-37050 x^2+e^{2 x} \left (-75 x^2+\left (-3 x^2-15 x-39\right ) \log ^2(2)+\left (-30 x^2-150 x-390\right ) \log (2)-375 x-975\right )+e^x \left (75 x^4+750 x^3+3825 x^2+\left (3 x^4+30 x^3+153 x^2+390 x+507\right ) \log ^2(2)+\left (30 x^4+300 x^3+1530 x^2+3900 x+5070\right ) \log (2)+9750 x+12675\right )+\left (-x^6-15 x^5-114 x^4-515 x^3-1482 x^2-2535 x-2197\right ) \log ^2(2)+\left (-10 x^6-150 x^5-1140 x^4-5150 x^3-14820 x^2-25350 x-21970\right ) \log (2)-63375 x+e^{3 x} \left (25+\log ^2(2)+10 \log (2)\right )-54925} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 x^9 (5+\log (2))^2+60 x^8 (5+\log (2))^2+456 x^7 (5+\log (2))^2+2061 x^6 (5+\log (2))^2+5943 x^5 (5+\log (2))^2+10254 x^4 (5+\log (2))^2+9303 x^3 (5+\log (2))^2-e^{3 x} \left (4 x^3+1\right ) (5+\log (2))^2+3 x^2 \left (12351+494 \log ^2(2)+4940 \log (2)\right )+3 e^{2 x} \left (4 x^5+20 x^4+52 x^3+x^2+5 x+13\right ) (5+\log (2))^2-e^x \left (12 x^7 (5+\log (2))^2+120 x^6 (5+\log (2))^2+612 x^5 (5+\log (2))^2+1563 x^4 (5+\log (2))^2+2058 x^3 (5+\log (2))^2+153 x^2 (5+\log (2))^2+x \left (9752+390 \log ^2(2)+3900 \log (2)\right )+12674+507 \log ^2(2)+5070 \log (2)\right )+5 x \left (12676+507 \log ^2(2)+5070 \log (2)\right )+13 \left (4224+169 \log ^2(2)+1690 \log (2)\right )}{\left (x^2+5 x-e^x+13\right )^3 (5+\log (2))^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \frac {4 (5+\log (2))^2 x^9+60 (5+\log (2))^2 x^8+456 (5+\log (2))^2 x^7+2061 (5+\log (2))^2 x^6+5943 (5+\log (2))^2 x^5+10254 (5+\log (2))^2 x^4+9303 (5+\log (2))^2 x^3+3 \left (12351+4940 \log (2)+494 \log ^2(2)\right ) x^2+5 \left (12676+5070 \log (2)+507 \log ^2(2)\right ) x-e^x \left (12 (5+\log (2))^2 x^7+120 (5+\log (2))^2 x^6+612 (5+\log (2))^2 x^5+1563 (5+\log (2))^2 x^4+2058 (5+\log (2))^2 x^3+153 (5+\log (2))^2 x^2+2 \left (4876+1950 \log (2)+195 \log ^2(2)\right ) x+507 \log ^2(2)+5070 \log (2)+12674\right )+13 \left (4224+1690 \log (2)+169 \log ^2(2)\right )-e^{3 x} \left (4 x^3+1\right ) (5+\log (2))^2+3 e^{2 x} \left (4 x^5+20 x^4+52 x^3+x^2+5 x+13\right ) (5+\log (2))^2}{\left (x^2+5 x-e^x+13\right )^3}dx}{(5+\log (2))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {\int \left (\frac {2 x-1}{\left (x^2+5 x-e^x+13\right )^2}-\frac {2 x \left (x^2+3 x+8\right )}{\left (x^2+5 x-e^x+13\right )^3}+\left (4 x^3+1\right ) (5+\log (2))^2\right )dx}{(5+\log (2))^2}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {-\int \frac {1}{\left (-x^2-5 x+e^x-13\right )^2}dx-16 \int \frac {x}{\left (x^2+5 x-e^x+13\right )^3}dx-6 \int \frac {x^2}{\left (x^2+5 x-e^x+13\right )^3}dx+2 \int \frac {x}{\left (x^2+5 x-e^x+13\right )^2}dx-2 \int \frac {x^3}{\left (x^2+5 x-e^x+13\right )^3}dx+x^4 (5+\log (2))^2+x (5+\log (2))^2}{(5+\log (2))^2}\) |
Input:
Int[(-54912 - 63380*x - 37053*x^2 - 232575*x^3 - 256350*x^4 - 148575*x^5 - 51525*x^6 - 11400*x^7 - 1500*x^8 - 100*x^9 + (-21970 - 25350*x - 14820*x^ 2 - 93030*x^3 - 102540*x^4 - 59430*x^5 - 20610*x^6 - 4560*x^7 - 600*x^8 - 40*x^9)*Log[2] + (-2197 - 2535*x - 1482*x^2 - 9303*x^3 - 10254*x^4 - 5943* x^5 - 2061*x^6 - 456*x^7 - 60*x^8 - 4*x^9)*Log[2]^2 + E^(3*x)*(25 + 100*x^ 3 + (10 + 40*x^3)*Log[2] + (1 + 4*x^3)*Log[2]^2) + E^(2*x)*(-975 - 375*x - 75*x^2 - 3900*x^3 - 1500*x^4 - 300*x^5 + (-390 - 150*x - 30*x^2 - 1560*x^ 3 - 600*x^4 - 120*x^5)*Log[2] + (-39 - 15*x - 3*x^2 - 156*x^3 - 60*x^4 - 1 2*x^5)*Log[2]^2) + E^x*(12674 + 9752*x + 3825*x^2 + 51450*x^3 + 39075*x^4 + 15300*x^5 + 3000*x^6 + 300*x^7 + (5070 + 3900*x + 1530*x^2 + 20580*x^3 + 15630*x^4 + 6120*x^5 + 1200*x^6 + 120*x^7)*Log[2] + (507 + 390*x + 153*x^ 2 + 2058*x^3 + 1563*x^4 + 612*x^5 + 120*x^6 + 12*x^7)*Log[2]^2))/(-54925 - 63375*x - 37050*x^2 - 12875*x^3 - 2850*x^4 - 375*x^5 - 25*x^6 + (-21970 - 25350*x - 14820*x^2 - 5150*x^3 - 1140*x^4 - 150*x^5 - 10*x^6)*Log[2] + (- 2197 - 2535*x - 1482*x^2 - 515*x^3 - 114*x^4 - 15*x^5 - x^6)*Log[2]^2 + E^ (3*x)*(25 + 10*Log[2] + Log[2]^2) + E^(2*x)*(-975 - 375*x - 75*x^2 + (-390 - 150*x - 30*x^2)*Log[2] + (-39 - 15*x - 3*x^2)*Log[2]^2) + E^x*(12675 + 9750*x + 3825*x^2 + 750*x^3 + 75*x^4 + (5070 + 3900*x + 1530*x^2 + 300*x^3 + 30*x^4)*Log[2] + (507 + 390*x + 153*x^2 + 30*x^3 + 3*x^4)*Log[2]^2)),x]
Output:
$Aborted
Time = 22.58 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.21
| method | result | size |
| risch | \(x^{4}+x -\frac {x}{\left (\ln \left (2\right )^{2}+10 \ln \left (2\right )+25\right ) \left (x^{2}+5 x -{\mathrm e}^{x}+13\right )^{2}}\) | \(35\) |
| parallelrisch | \(\frac {4224 x +510 x^{6} \ln \left (2\right )+1310 x^{5} \ln \left (2\right )+x \ln \left (2\right )^{2} {\mathrm e}^{2 x}+131 x^{5} \ln \left (2\right )^{2}+51 x^{3} \ln \left (2\right )^{2}-50 x^{6} {\mathrm e}^{x}+169 x \ln \left (2\right )^{2}+510 x^{3} \ln \left (2\right )+1790 x^{4} \ln \left (2\right )+1300 x^{2} \ln \left (2\right )+100 x^{7} \ln \left (2\right )+10 x^{8} \ln \left (2\right )+1690 x \ln \left (2\right )-250 \,{\mathrm e}^{x} x^{2}-650 \,{\mathrm e}^{x} x^{4}-50 \,{\mathrm e}^{x} x^{3}-260 x \ln \left (2\right ) {\mathrm e}^{x}+25 x^{4} {\mathrm e}^{2 x}+179 x^{4} \ln \left (2\right )^{2}-100 x^{2} \ln \left (2\right ) {\mathrm e}^{x}+25 x \,{\mathrm e}^{2 x}+25 x^{8}+250 x^{7}+130 x^{2} \ln \left (2\right )^{2}-650 \,{\mathrm e}^{x} x -250 x^{5} {\mathrm e}^{x}+1275 x^{6}+3250 x^{2}+1275 x^{3}+4475 x^{4}+3275 x^{5}-20 x^{3} \ln \left (2\right ) {\mathrm e}^{x}-2 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{3}-260 \,{\mathrm e}^{x} x^{4} \ln \left (2\right )-100 \ln \left (2\right ) {\mathrm e}^{x} x^{5}-20 \ln \left (2\right ) {\mathrm e}^{x} x^{6}+\ln \left (2\right )^{2} x^{8}+10 \ln \left (2\right )^{2} x^{7}+51 \ln \left (2\right )^{2} x^{6}-10 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{5}-2 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{6}+\ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{4}+10 \ln \left (2\right ) {\mathrm e}^{2 x} x^{4}-26 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{4}-10 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{2}-26 \ln \left (2\right )^{2} {\mathrm e}^{x} x +10 \ln \left (2\right ) {\mathrm e}^{2 x} x}{\left (\ln \left (2\right )^{2}+10 \ln \left (2\right )+25\right ) \left (x^{4}+10 x^{3}-2 \,{\mathrm e}^{x} x^{2}+51 x^{2}-10 \,{\mathrm e}^{x} x +{\mathrm e}^{2 x}+130 x -26 \,{\mathrm e}^{x}+169\right )}\) | \(430\) |
Input:
int((((4*x^3+1)*ln(2)^2+(40*x^3+10)*ln(2)+100*x^3+25)*exp(x)^3+((-12*x^5-6 0*x^4-156*x^3-3*x^2-15*x-39)*ln(2)^2+(-120*x^5-600*x^4-1560*x^3-30*x^2-150 *x-390)*ln(2)-300*x^5-1500*x^4-3900*x^3-75*x^2-375*x-975)*exp(x)^2+((12*x^ 7+120*x^6+612*x^5+1563*x^4+2058*x^3+153*x^2+390*x+507)*ln(2)^2+(120*x^7+12 00*x^6+6120*x^5+15630*x^4+20580*x^3+1530*x^2+3900*x+5070)*ln(2)+300*x^7+30 00*x^6+15300*x^5+39075*x^4+51450*x^3+3825*x^2+9752*x+12674)*exp(x)+(-4*x^9 -60*x^8-456*x^7-2061*x^6-5943*x^5-10254*x^4-9303*x^3-1482*x^2-2535*x-2197) *ln(2)^2+(-40*x^9-600*x^8-4560*x^7-20610*x^6-59430*x^5-102540*x^4-93030*x^ 3-14820*x^2-25350*x-21970)*ln(2)-100*x^9-1500*x^8-11400*x^7-51525*x^6-1485 75*x^5-256350*x^4-232575*x^3-37053*x^2-63380*x-54912)/((ln(2)^2+10*ln(2)+2 5)*exp(x)^3+((-3*x^2-15*x-39)*ln(2)^2+(-30*x^2-150*x-390)*ln(2)-75*x^2-375 *x-975)*exp(x)^2+((3*x^4+30*x^3+153*x^2+390*x+507)*ln(2)^2+(30*x^4+300*x^3 +1530*x^2+3900*x+5070)*ln(2)+75*x^4+750*x^3+3825*x^2+9750*x+12675)*exp(x)+ (-x^6-15*x^5-114*x^4-515*x^3-1482*x^2-2535*x-2197)*ln(2)^2+(-10*x^6-150*x^ 5-1140*x^4-5150*x^3-14820*x^2-25350*x-21970)*ln(2)-25*x^6-375*x^5-2850*x^4 -12875*x^3-37050*x^2-63375*x-54925),x,method=_RETURNVERBOSE)
Output:
x^4+x-x/(ln(2)^2+10*ln(2)+25)/(x^2+5*x-exp(x)+13)^2
Leaf count of result is larger than twice the leaf count of optimal. 369 vs. \(2 (30) = 60\).
Time = 0.11 (sec) , antiderivative size = 369, normalized size of antiderivative = 12.72 \[ \int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+\left (-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9\right ) \log (2)+\left (-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9\right ) \log ^2(2)+e^{3 x} \left (25+100 x^3+\left (10+40 x^3\right ) \log (2)+\left (1+4 x^3\right ) \log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+\left (-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5\right ) \log (2)+\left (-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5\right ) \log ^2(2)\right )+e^x \left (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+\left (5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7\right ) \log (2)+\left (507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7\right ) \log ^2(2)\right )}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+\left (-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6\right ) \log (2)+\left (-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6\right ) \log ^2(2)+e^{3 x} \left (25+10 \log (2)+\log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2+\left (-390-150 x-30 x^2\right ) \log (2)+\left (-39-15 x-3 x^2\right ) \log ^2(2)\right )+e^x \left (12675+9750 x+3825 x^2+750 x^3+75 x^4+\left (5070+3900 x+1530 x^2+300 x^3+30 x^4\right ) \log (2)+\left (507+390 x+153 x^2+30 x^3+3 x^4\right ) \log ^2(2)\right )} \, dx=\frac {25 \, x^{8} + 250 \, x^{7} + 1275 \, x^{6} + 3275 \, x^{5} + 4475 \, x^{4} + 1275 \, x^{3} + {\left (x^{8} + 10 \, x^{7} + 51 \, x^{6} + 131 \, x^{5} + 179 \, x^{4} + 51 \, x^{3} + 130 \, x^{2} + 169 \, x\right )} \log \left (2\right )^{2} + 3250 \, x^{2} + {\left (25 \, x^{4} + {\left (x^{4} + x\right )} \log \left (2\right )^{2} + 10 \, {\left (x^{4} + x\right )} \log \left (2\right ) + 25 \, x\right )} e^{\left (2 \, x\right )} - 2 \, {\left (25 \, x^{6} + 125 \, x^{5} + 325 \, x^{4} + 25 \, x^{3} + {\left (x^{6} + 5 \, x^{5} + 13 \, x^{4} + x^{3} + 5 \, x^{2} + 13 \, x\right )} \log \left (2\right )^{2} + 125 \, x^{2} + 10 \, {\left (x^{6} + 5 \, x^{5} + 13 \, x^{4} + x^{3} + 5 \, x^{2} + 13 \, x\right )} \log \left (2\right ) + 325 \, x\right )} e^{x} + 10 \, {\left (x^{8} + 10 \, x^{7} + 51 \, x^{6} + 131 \, x^{5} + 179 \, x^{4} + 51 \, x^{3} + 130 \, x^{2} + 169 \, x\right )} \log \left (2\right ) + 4224 \, x}{25 \, x^{4} + 250 \, x^{3} + {\left (x^{4} + 10 \, x^{3} + 51 \, x^{2} + 130 \, x + 169\right )} \log \left (2\right )^{2} + 1275 \, x^{2} + {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} e^{\left (2 \, x\right )} - 2 \, {\left ({\left (x^{2} + 5 \, x + 13\right )} \log \left (2\right )^{2} + 25 \, x^{2} + 10 \, {\left (x^{2} + 5 \, x + 13\right )} \log \left (2\right ) + 125 \, x + 325\right )} e^{x} + 10 \, {\left (x^{4} + 10 \, x^{3} + 51 \, x^{2} + 130 \, x + 169\right )} \log \left (2\right ) + 3250 \, x + 4225} \] Input:
integrate((((4*x^3+1)*log(2)^2+(40*x^3+10)*log(2)+100*x^3+25)*exp(x)^3+((- 12*x^5-60*x^4-156*x^3-3*x^2-15*x-39)*log(2)^2+(-120*x^5-600*x^4-1560*x^3-3 0*x^2-150*x-390)*log(2)-300*x^5-1500*x^4-3900*x^3-75*x^2-375*x-975)*exp(x) ^2+((12*x^7+120*x^6+612*x^5+1563*x^4+2058*x^3+153*x^2+390*x+507)*log(2)^2+ (120*x^7+1200*x^6+6120*x^5+15630*x^4+20580*x^3+1530*x^2+3900*x+5070)*log(2 )+300*x^7+3000*x^6+15300*x^5+39075*x^4+51450*x^3+3825*x^2+9752*x+12674)*ex p(x)+(-4*x^9-60*x^8-456*x^7-2061*x^6-5943*x^5-10254*x^4-9303*x^3-1482*x^2- 2535*x-2197)*log(2)^2+(-40*x^9-600*x^8-4560*x^7-20610*x^6-59430*x^5-102540 *x^4-93030*x^3-14820*x^2-25350*x-21970)*log(2)-100*x^9-1500*x^8-11400*x^7- 51525*x^6-148575*x^5-256350*x^4-232575*x^3-37053*x^2-63380*x-54912)/((log( 2)^2+10*log(2)+25)*exp(x)^3+((-3*x^2-15*x-39)*log(2)^2+(-30*x^2-150*x-390) *log(2)-75*x^2-375*x-975)*exp(x)^2+((3*x^4+30*x^3+153*x^2+390*x+507)*log(2 )^2+(30*x^4+300*x^3+1530*x^2+3900*x+5070)*log(2)+75*x^4+750*x^3+3825*x^2+9 750*x+12675)*exp(x)+(-x^6-15*x^5-114*x^4-515*x^3-1482*x^2-2535*x-2197)*log (2)^2+(-10*x^6-150*x^5-1140*x^4-5150*x^3-14820*x^2-25350*x-21970)*log(2)-2 5*x^6-375*x^5-2850*x^4-12875*x^3-37050*x^2-63375*x-54925),x, algorithm="fr icas")
Output:
(25*x^8 + 250*x^7 + 1275*x^6 + 3275*x^5 + 4475*x^4 + 1275*x^3 + (x^8 + 10* x^7 + 51*x^6 + 131*x^5 + 179*x^4 + 51*x^3 + 130*x^2 + 169*x)*log(2)^2 + 32 50*x^2 + (25*x^4 + (x^4 + x)*log(2)^2 + 10*(x^4 + x)*log(2) + 25*x)*e^(2*x ) - 2*(25*x^6 + 125*x^5 + 325*x^4 + 25*x^3 + (x^6 + 5*x^5 + 13*x^4 + x^3 + 5*x^2 + 13*x)*log(2)^2 + 125*x^2 + 10*(x^6 + 5*x^5 + 13*x^4 + x^3 + 5*x^2 + 13*x)*log(2) + 325*x)*e^x + 10*(x^8 + 10*x^7 + 51*x^6 + 131*x^5 + 179*x ^4 + 51*x^3 + 130*x^2 + 169*x)*log(2) + 4224*x)/(25*x^4 + 250*x^3 + (x^4 + 10*x^3 + 51*x^2 + 130*x + 169)*log(2)^2 + 1275*x^2 + (log(2)^2 + 10*log(2 ) + 25)*e^(2*x) - 2*((x^2 + 5*x + 13)*log(2)^2 + 25*x^2 + 10*(x^2 + 5*x + 13)*log(2) + 125*x + 325)*e^x + 10*(x^4 + 10*x^3 + 51*x^2 + 130*x + 169)*l og(2) + 3250*x + 4225)
Leaf count of result is larger than twice the leaf count of optimal. 185 vs. \(2 (26) = 52\).
Time = 0.42 (sec) , antiderivative size = 185, normalized size of antiderivative = 6.38 \[ \int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+\left (-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9\right ) \log (2)+\left (-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9\right ) \log ^2(2)+e^{3 x} \left (25+100 x^3+\left (10+40 x^3\right ) \log (2)+\left (1+4 x^3\right ) \log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+\left (-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5\right ) \log (2)+\left (-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5\right ) \log ^2(2)\right )+e^x \left (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+\left (5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7\right ) \log (2)+\left (507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7\right ) \log ^2(2)\right )}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+\left (-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6\right ) \log (2)+\left (-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6\right ) \log ^2(2)+e^{3 x} \left (25+10 \log (2)+\log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2+\left (-390-150 x-30 x^2\right ) \log (2)+\left (-39-15 x-3 x^2\right ) \log ^2(2)\right )+e^x \left (12675+9750 x+3825 x^2+750 x^3+75 x^4+\left (5070+3900 x+1530 x^2+300 x^3+30 x^4\right ) \log (2)+\left (507+390 x+153 x^2+30 x^3+3 x^4\right ) \log ^2(2)\right )} \, dx=x^{4} + x - \frac {x}{x^{4} \log {\left (2 \right )}^{2} + 10 x^{4} \log {\left (2 \right )} + 25 x^{4} + 10 x^{3} \log {\left (2 \right )}^{2} + 100 x^{3} \log {\left (2 \right )} + 250 x^{3} + 51 x^{2} \log {\left (2 \right )}^{2} + 510 x^{2} \log {\left (2 \right )} + 1275 x^{2} + 130 x \log {\left (2 \right )}^{2} + 1300 x \log {\left (2 \right )} + 3250 x + \left (- 50 x^{2} - 20 x^{2} \log {\left (2 \right )} - 2 x^{2} \log {\left (2 \right )}^{2} - 250 x - 100 x \log {\left (2 \right )} - 10 x \log {\left (2 \right )}^{2} - 650 - 260 \log {\left (2 \right )} - 26 \log {\left (2 \right )}^{2}\right ) e^{x} + \left (\log {\left (2 \right )}^{2} + 10 \log {\left (2 \right )} + 25\right ) e^{2 x} + 169 \log {\left (2 \right )}^{2} + 1690 \log {\left (2 \right )} + 4225} \] Input:
integrate((((4*x**3+1)*ln(2)**2+(40*x**3+10)*ln(2)+100*x**3+25)*exp(x)**3+ ((-12*x**5-60*x**4-156*x**3-3*x**2-15*x-39)*ln(2)**2+(-120*x**5-600*x**4-1 560*x**3-30*x**2-150*x-390)*ln(2)-300*x**5-1500*x**4-3900*x**3-75*x**2-375 *x-975)*exp(x)**2+((12*x**7+120*x**6+612*x**5+1563*x**4+2058*x**3+153*x**2 +390*x+507)*ln(2)**2+(120*x**7+1200*x**6+6120*x**5+15630*x**4+20580*x**3+1 530*x**2+3900*x+5070)*ln(2)+300*x**7+3000*x**6+15300*x**5+39075*x**4+51450 *x**3+3825*x**2+9752*x+12674)*exp(x)+(-4*x**9-60*x**8-456*x**7-2061*x**6-5 943*x**5-10254*x**4-9303*x**3-1482*x**2-2535*x-2197)*ln(2)**2+(-40*x**9-60 0*x**8-4560*x**7-20610*x**6-59430*x**5-102540*x**4-93030*x**3-14820*x**2-2 5350*x-21970)*ln(2)-100*x**9-1500*x**8-11400*x**7-51525*x**6-148575*x**5-2 56350*x**4-232575*x**3-37053*x**2-63380*x-54912)/((ln(2)**2+10*ln(2)+25)*e xp(x)**3+((-3*x**2-15*x-39)*ln(2)**2+(-30*x**2-150*x-390)*ln(2)-75*x**2-37 5*x-975)*exp(x)**2+((3*x**4+30*x**3+153*x**2+390*x+507)*ln(2)**2+(30*x**4+ 300*x**3+1530*x**2+3900*x+5070)*ln(2)+75*x**4+750*x**3+3825*x**2+9750*x+12 675)*exp(x)+(-x**6-15*x**5-114*x**4-515*x**3-1482*x**2-2535*x-2197)*ln(2)* *2+(-10*x**6-150*x**5-1140*x**4-5150*x**3-14820*x**2-25350*x-21970)*ln(2)- 25*x**6-375*x**5-2850*x**4-12875*x**3-37050*x**2-63375*x-54925),x)
Output:
x**4 + x - x/(x**4*log(2)**2 + 10*x**4*log(2) + 25*x**4 + 10*x**3*log(2)** 2 + 100*x**3*log(2) + 250*x**3 + 51*x**2*log(2)**2 + 510*x**2*log(2) + 127 5*x**2 + 130*x*log(2)**2 + 1300*x*log(2) + 3250*x + (-50*x**2 - 20*x**2*lo g(2) - 2*x**2*log(2)**2 - 250*x - 100*x*log(2) - 10*x*log(2)**2 - 650 - 26 0*log(2) - 26*log(2)**2)*exp(x) + (log(2)**2 + 10*log(2) + 25)*exp(2*x) + 169*log(2)**2 + 1690*log(2) + 4225)
Leaf count of result is larger than twice the leaf count of optimal. 372 vs. \(2 (30) = 60\).
Time = 0.63 (sec) , antiderivative size = 372, normalized size of antiderivative = 12.83 \[ \int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+\left (-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9\right ) \log (2)+\left (-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9\right ) \log ^2(2)+e^{3 x} \left (25+100 x^3+\left (10+40 x^3\right ) \log (2)+\left (1+4 x^3\right ) \log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+\left (-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5\right ) \log (2)+\left (-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5\right ) \log ^2(2)\right )+e^x \left (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+\left (5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7\right ) \log (2)+\left (507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7\right ) \log ^2(2)\right )}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+\left (-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6\right ) \log (2)+\left (-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6\right ) \log ^2(2)+e^{3 x} \left (25+10 \log (2)+\log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2+\left (-390-150 x-30 x^2\right ) \log (2)+\left (-39-15 x-3 x^2\right ) \log ^2(2)\right )+e^x \left (12675+9750 x+3825 x^2+750 x^3+75 x^4+\left (5070+3900 x+1530 x^2+300 x^3+30 x^4\right ) \log (2)+\left (507+390 x+153 x^2+30 x^3+3 x^4\right ) \log ^2(2)\right )} \, dx =\text {Too large to display} \] Input:
integrate((((4*x^3+1)*log(2)^2+(40*x^3+10)*log(2)+100*x^3+25)*exp(x)^3+((- 12*x^5-60*x^4-156*x^3-3*x^2-15*x-39)*log(2)^2+(-120*x^5-600*x^4-1560*x^3-3 0*x^2-150*x-390)*log(2)-300*x^5-1500*x^4-3900*x^3-75*x^2-375*x-975)*exp(x) ^2+((12*x^7+120*x^6+612*x^5+1563*x^4+2058*x^3+153*x^2+390*x+507)*log(2)^2+ (120*x^7+1200*x^6+6120*x^5+15630*x^4+20580*x^3+1530*x^2+3900*x+5070)*log(2 )+300*x^7+3000*x^6+15300*x^5+39075*x^4+51450*x^3+3825*x^2+9752*x+12674)*ex p(x)+(-4*x^9-60*x^8-456*x^7-2061*x^6-5943*x^5-10254*x^4-9303*x^3-1482*x^2- 2535*x-2197)*log(2)^2+(-40*x^9-600*x^8-4560*x^7-20610*x^6-59430*x^5-102540 *x^4-93030*x^3-14820*x^2-25350*x-21970)*log(2)-100*x^9-1500*x^8-11400*x^7- 51525*x^6-148575*x^5-256350*x^4-232575*x^3-37053*x^2-63380*x-54912)/((log( 2)^2+10*log(2)+25)*exp(x)^3+((-3*x^2-15*x-39)*log(2)^2+(-30*x^2-150*x-390) *log(2)-75*x^2-375*x-975)*exp(x)^2+((3*x^4+30*x^3+153*x^2+390*x+507)*log(2 )^2+(30*x^4+300*x^3+1530*x^2+3900*x+5070)*log(2)+75*x^4+750*x^3+3825*x^2+9 750*x+12675)*exp(x)+(-x^6-15*x^5-114*x^4-515*x^3-1482*x^2-2535*x-2197)*log (2)^2+(-10*x^6-150*x^5-1140*x^4-5150*x^3-14820*x^2-25350*x-21970)*log(2)-2 5*x^6-375*x^5-2850*x^4-12875*x^3-37050*x^2-63375*x-54925),x, algorithm="ma xima")
Output:
((log(2)^2 + 10*log(2) + 25)*x^8 + 10*(log(2)^2 + 10*log(2) + 25)*x^7 + 51 *(log(2)^2 + 10*log(2) + 25)*x^6 + 131*(log(2)^2 + 10*log(2) + 25)*x^5 + 1 79*(log(2)^2 + 10*log(2) + 25)*x^4 + 51*(log(2)^2 + 10*log(2) + 25)*x^3 + 130*(log(2)^2 + 10*log(2) + 25)*x^2 + (169*log(2)^2 + 1690*log(2) + 4224)* x + ((log(2)^2 + 10*log(2) + 25)*x^4 + (log(2)^2 + 10*log(2) + 25)*x)*e^(2 *x) - 2*((log(2)^2 + 10*log(2) + 25)*x^6 + 5*(log(2)^2 + 10*log(2) + 25)*x ^5 + 13*(log(2)^2 + 10*log(2) + 25)*x^4 + (log(2)^2 + 10*log(2) + 25)*x^3 + 5*(log(2)^2 + 10*log(2) + 25)*x^2 + 13*(log(2)^2 + 10*log(2) + 25)*x)*e^ x)/((log(2)^2 + 10*log(2) + 25)*x^4 + 10*(log(2)^2 + 10*log(2) + 25)*x^3 + 51*(log(2)^2 + 10*log(2) + 25)*x^2 + 130*(log(2)^2 + 10*log(2) + 25)*x + (log(2)^2 + 10*log(2) + 25)*e^(2*x) - 2*((log(2)^2 + 10*log(2) + 25)*x^2 + 5*(log(2)^2 + 10*log(2) + 25)*x + 13*log(2)^2 + 130*log(2) + 325)*e^x + 1 69*log(2)^2 + 1690*log(2) + 4225)
Leaf count of result is larger than twice the leaf count of optimal. 557 vs. \(2 (30) = 60\).
Time = 0.22 (sec) , antiderivative size = 557, normalized size of antiderivative = 19.21 \[ \int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+\left (-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9\right ) \log (2)+\left (-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9\right ) \log ^2(2)+e^{3 x} \left (25+100 x^3+\left (10+40 x^3\right ) \log (2)+\left (1+4 x^3\right ) \log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+\left (-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5\right ) \log (2)+\left (-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5\right ) \log ^2(2)\right )+e^x \left (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+\left (5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7\right ) \log (2)+\left (507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7\right ) \log ^2(2)\right )}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+\left (-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6\right ) \log (2)+\left (-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6\right ) \log ^2(2)+e^{3 x} \left (25+10 \log (2)+\log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2+\left (-390-150 x-30 x^2\right ) \log (2)+\left (-39-15 x-3 x^2\right ) \log ^2(2)\right )+e^x \left (12675+9750 x+3825 x^2+750 x^3+75 x^4+\left (5070+3900 x+1530 x^2+300 x^3+30 x^4\right ) \log (2)+\left (507+390 x+153 x^2+30 x^3+3 x^4\right ) \log ^2(2)\right )} \, dx =\text {Too large to display} \] Input:
integrate((((4*x^3+1)*log(2)^2+(40*x^3+10)*log(2)+100*x^3+25)*exp(x)^3+((- 12*x^5-60*x^4-156*x^3-3*x^2-15*x-39)*log(2)^2+(-120*x^5-600*x^4-1560*x^3-3 0*x^2-150*x-390)*log(2)-300*x^5-1500*x^4-3900*x^3-75*x^2-375*x-975)*exp(x) ^2+((12*x^7+120*x^6+612*x^5+1563*x^4+2058*x^3+153*x^2+390*x+507)*log(2)^2+ (120*x^7+1200*x^6+6120*x^5+15630*x^4+20580*x^3+1530*x^2+3900*x+5070)*log(2 )+300*x^7+3000*x^6+15300*x^5+39075*x^4+51450*x^3+3825*x^2+9752*x+12674)*ex p(x)+(-4*x^9-60*x^8-456*x^7-2061*x^6-5943*x^5-10254*x^4-9303*x^3-1482*x^2- 2535*x-2197)*log(2)^2+(-40*x^9-600*x^8-4560*x^7-20610*x^6-59430*x^5-102540 *x^4-93030*x^3-14820*x^2-25350*x-21970)*log(2)-100*x^9-1500*x^8-11400*x^7- 51525*x^6-148575*x^5-256350*x^4-232575*x^3-37053*x^2-63380*x-54912)/((log( 2)^2+10*log(2)+25)*exp(x)^3+((-3*x^2-15*x-39)*log(2)^2+(-30*x^2-150*x-390) *log(2)-75*x^2-375*x-975)*exp(x)^2+((3*x^4+30*x^3+153*x^2+390*x+507)*log(2 )^2+(30*x^4+300*x^3+1530*x^2+3900*x+5070)*log(2)+75*x^4+750*x^3+3825*x^2+9 750*x+12675)*exp(x)+(-x^6-15*x^5-114*x^4-515*x^3-1482*x^2-2535*x-2197)*log (2)^2+(-10*x^6-150*x^5-1140*x^4-5150*x^3-14820*x^2-25350*x-21970)*log(2)-2 5*x^6-375*x^5-2850*x^4-12875*x^3-37050*x^2-63375*x-54925),x, algorithm="gi ac")
Output:
(x^8*log(2)^2 + 10*x^8*log(2) + 10*x^7*log(2)^2 - 2*x^6*e^x*log(2)^2 + 25* x^8 + 100*x^7*log(2) - 20*x^6*e^x*log(2) + 51*x^6*log(2)^2 - 10*x^5*e^x*lo g(2)^2 + 250*x^7 - 50*x^6*e^x + 510*x^6*log(2) - 100*x^5*e^x*log(2) + 131* x^5*log(2)^2 + x^4*e^(2*x)*log(2)^2 - 26*x^4*e^x*log(2)^2 + 1275*x^6 - 250 *x^5*e^x + 1310*x^5*log(2) + 10*x^4*e^(2*x)*log(2) - 260*x^4*e^x*log(2) + 179*x^4*log(2)^2 - 2*x^3*e^x*log(2)^2 + 3275*x^5 + 25*x^4*e^(2*x) - 650*x^ 4*e^x + 1790*x^4*log(2) - 20*x^3*e^x*log(2) + 51*x^3*log(2)^2 - 10*x^2*e^x *log(2)^2 + 4475*x^4 - 50*x^3*e^x + 510*x^3*log(2) - 100*x^2*e^x*log(2) + 130*x^2*log(2)^2 + x*e^(2*x)*log(2)^2 - 26*x*e^x*log(2)^2 + 1275*x^3 - 250 *x^2*e^x + 1300*x^2*log(2) + 10*x*e^(2*x)*log(2) - 260*x*e^x*log(2) + 169* x*log(2)^2 + 3250*x^2 + 25*x*e^(2*x) - 650*x*e^x + 1690*x*log(2) + 4224*x) /(x^4*log(2)^2 + 10*x^4*log(2) + 10*x^3*log(2)^2 - 2*x^2*e^x*log(2)^2 + 25 *x^4 + 100*x^3*log(2) - 20*x^2*e^x*log(2) + 51*x^2*log(2)^2 - 10*x*e^x*log (2)^2 + 250*x^3 - 50*x^2*e^x + 510*x^2*log(2) - 100*x*e^x*log(2) + 130*x*l og(2)^2 + e^(2*x)*log(2)^2 - 26*e^x*log(2)^2 + 1275*x^2 - 250*x*e^x + 1300 *x*log(2) + 10*e^(2*x)*log(2) - 260*e^x*log(2) + 169*log(2)^2 + 3250*x + 2 5*e^(2*x) - 650*e^x + 1690*log(2) + 4225)
Timed out. \[ \int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+\left (-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9\right ) \log (2)+\left (-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9\right ) \log ^2(2)+e^{3 x} \left (25+100 x^3+\left (10+40 x^3\right ) \log (2)+\left (1+4 x^3\right ) \log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+\left (-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5\right ) \log (2)+\left (-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5\right ) \log ^2(2)\right )+e^x \left (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+\left (5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7\right ) \log (2)+\left (507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7\right ) \log ^2(2)\right )}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+\left (-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6\right ) \log (2)+\left (-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6\right ) \log ^2(2)+e^{3 x} \left (25+10 \log (2)+\log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2+\left (-390-150 x-30 x^2\right ) \log (2)+\left (-39-15 x-3 x^2\right ) \log ^2(2)\right )+e^x \left (12675+9750 x+3825 x^2+750 x^3+75 x^4+\left (5070+3900 x+1530 x^2+300 x^3+30 x^4\right ) \log (2)+\left (507+390 x+153 x^2+30 x^3+3 x^4\right ) \log ^2(2)\right )} \, dx=\int \frac {63380\,x+{\ln \left (2\right )}^2\,\left (4\,x^9+60\,x^8+456\,x^7+2061\,x^6+5943\,x^5+10254\,x^4+9303\,x^3+1482\,x^2+2535\,x+2197\right )-{\mathrm {e}}^{3\,x}\,\left (\ln \left (2\right )\,\left (40\,x^3+10\right )+{\ln \left (2\right )}^2\,\left (4\,x^3+1\right )+100\,x^3+25\right )-{\mathrm {e}}^x\,\left (9752\,x+\ln \left (2\right )\,\left (120\,x^7+1200\,x^6+6120\,x^5+15630\,x^4+20580\,x^3+1530\,x^2+3900\,x+5070\right )+{\ln \left (2\right )}^2\,\left (12\,x^7+120\,x^6+612\,x^5+1563\,x^4+2058\,x^3+153\,x^2+390\,x+507\right )+3825\,x^2+51450\,x^3+39075\,x^4+15300\,x^5+3000\,x^6+300\,x^7+12674\right )+\ln \left (2\right )\,\left (40\,x^9+600\,x^8+4560\,x^7+20610\,x^6+59430\,x^5+102540\,x^4+93030\,x^3+14820\,x^2+25350\,x+21970\right )+{\mathrm {e}}^{2\,x}\,\left (375\,x+{\ln \left (2\right )}^2\,\left (12\,x^5+60\,x^4+156\,x^3+3\,x^2+15\,x+39\right )+75\,x^2+3900\,x^3+1500\,x^4+300\,x^5+\ln \left (2\right )\,\left (120\,x^5+600\,x^4+1560\,x^3+30\,x^2+150\,x+390\right )+975\right )+37053\,x^2+232575\,x^3+256350\,x^4+148575\,x^5+51525\,x^6+11400\,x^7+1500\,x^8+100\,x^9+54912}{63375\,x+\ln \left (2\right )\,\left (10\,x^6+150\,x^5+1140\,x^4+5150\,x^3+14820\,x^2+25350\,x+21970\right )+{\ln \left (2\right )}^2\,\left (x^6+15\,x^5+114\,x^4+515\,x^3+1482\,x^2+2535\,x+2197\right )-{\mathrm {e}}^{3\,x}\,\left (10\,\ln \left (2\right )+{\ln \left (2\right )}^2+25\right )-{\mathrm {e}}^x\,\left (9750\,x+{\ln \left (2\right )}^2\,\left (3\,x^4+30\,x^3+153\,x^2+390\,x+507\right )+\ln \left (2\right )\,\left (30\,x^4+300\,x^3+1530\,x^2+3900\,x+5070\right )+3825\,x^2+750\,x^3+75\,x^4+12675\right )+37050\,x^2+12875\,x^3+2850\,x^4+375\,x^5+25\,x^6+{\mathrm {e}}^{2\,x}\,\left (375\,x+\ln \left (2\right )\,\left (30\,x^2+150\,x+390\right )+{\ln \left (2\right )}^2\,\left (3\,x^2+15\,x+39\right )+75\,x^2+975\right )+54925} \,d x \] Input:
int((63380*x + log(2)^2*(2535*x + 1482*x^2 + 9303*x^3 + 10254*x^4 + 5943*x ^5 + 2061*x^6 + 456*x^7 + 60*x^8 + 4*x^9 + 2197) - exp(3*x)*(log(2)*(40*x^ 3 + 10) + log(2)^2*(4*x^3 + 1) + 100*x^3 + 25) - exp(x)*(9752*x + log(2)*( 3900*x + 1530*x^2 + 20580*x^3 + 15630*x^4 + 6120*x^5 + 1200*x^6 + 120*x^7 + 5070) + log(2)^2*(390*x + 153*x^2 + 2058*x^3 + 1563*x^4 + 612*x^5 + 120* x^6 + 12*x^7 + 507) + 3825*x^2 + 51450*x^3 + 39075*x^4 + 15300*x^5 + 3000* x^6 + 300*x^7 + 12674) + log(2)*(25350*x + 14820*x^2 + 93030*x^3 + 102540* x^4 + 59430*x^5 + 20610*x^6 + 4560*x^7 + 600*x^8 + 40*x^9 + 21970) + exp(2 *x)*(375*x + log(2)^2*(15*x + 3*x^2 + 156*x^3 + 60*x^4 + 12*x^5 + 39) + 75 *x^2 + 3900*x^3 + 1500*x^4 + 300*x^5 + log(2)*(150*x + 30*x^2 + 1560*x^3 + 600*x^4 + 120*x^5 + 390) + 975) + 37053*x^2 + 232575*x^3 + 256350*x^4 + 1 48575*x^5 + 51525*x^6 + 11400*x^7 + 1500*x^8 + 100*x^9 + 54912)/(63375*x + log(2)*(25350*x + 14820*x^2 + 5150*x^3 + 1140*x^4 + 150*x^5 + 10*x^6 + 21 970) + log(2)^2*(2535*x + 1482*x^2 + 515*x^3 + 114*x^4 + 15*x^5 + x^6 + 21 97) - exp(3*x)*(10*log(2) + log(2)^2 + 25) - exp(x)*(9750*x + log(2)^2*(39 0*x + 153*x^2 + 30*x^3 + 3*x^4 + 507) + log(2)*(3900*x + 1530*x^2 + 300*x^ 3 + 30*x^4 + 5070) + 3825*x^2 + 750*x^3 + 75*x^4 + 12675) + 37050*x^2 + 12 875*x^3 + 2850*x^4 + 375*x^5 + 25*x^6 + exp(2*x)*(375*x + log(2)*(150*x + 30*x^2 + 390) + log(2)^2*(15*x + 3*x^2 + 39) + 75*x^2 + 975) + 54925),x)
Output:
int((63380*x + log(2)^2*(2535*x + 1482*x^2 + 9303*x^3 + 10254*x^4 + 5943*x ^5 + 2061*x^6 + 456*x^7 + 60*x^8 + 4*x^9 + 2197) - exp(3*x)*(log(2)*(40*x^ 3 + 10) + log(2)^2*(4*x^3 + 1) + 100*x^3 + 25) - exp(x)*(9752*x + log(2)*( 3900*x + 1530*x^2 + 20580*x^3 + 15630*x^4 + 6120*x^5 + 1200*x^6 + 120*x^7 + 5070) + log(2)^2*(390*x + 153*x^2 + 2058*x^3 + 1563*x^4 + 612*x^5 + 120* x^6 + 12*x^7 + 507) + 3825*x^2 + 51450*x^3 + 39075*x^4 + 15300*x^5 + 3000* x^6 + 300*x^7 + 12674) + log(2)*(25350*x + 14820*x^2 + 93030*x^3 + 102540* x^4 + 59430*x^5 + 20610*x^6 + 4560*x^7 + 600*x^8 + 40*x^9 + 21970) + exp(2 *x)*(375*x + log(2)^2*(15*x + 3*x^2 + 156*x^3 + 60*x^4 + 12*x^5 + 39) + 75 *x^2 + 3900*x^3 + 1500*x^4 + 300*x^5 + log(2)*(150*x + 30*x^2 + 1560*x^3 + 600*x^4 + 120*x^5 + 390) + 975) + 37053*x^2 + 232575*x^3 + 256350*x^4 + 1 48575*x^5 + 51525*x^6 + 11400*x^7 + 1500*x^8 + 100*x^9 + 54912)/(63375*x + log(2)*(25350*x + 14820*x^2 + 5150*x^3 + 1140*x^4 + 150*x^5 + 10*x^6 + 21 970) + log(2)^2*(2535*x + 1482*x^2 + 515*x^3 + 114*x^4 + 15*x^5 + x^6 + 21 97) - exp(3*x)*(10*log(2) + log(2)^2 + 25) - exp(x)*(9750*x + log(2)^2*(39 0*x + 153*x^2 + 30*x^3 + 3*x^4 + 507) + log(2)*(3900*x + 1530*x^2 + 300*x^ 3 + 30*x^4 + 5070) + 3825*x^2 + 750*x^3 + 75*x^4 + 12675) + 37050*x^2 + 12 875*x^3 + 2850*x^4 + 375*x^5 + 25*x^6 + exp(2*x)*(375*x + log(2)*(150*x + 30*x^2 + 390) + log(2)^2*(15*x + 3*x^2 + 39) + 75*x^2 + 975) + 54925), x)
Time = 0.20 (sec) , antiderivative size = 621, normalized size of antiderivative = 21.41 \[ \int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+\left (-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9\right ) \log (2)+\left (-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9\right ) \log ^2(2)+e^{3 x} \left (25+100 x^3+\left (10+40 x^3\right ) \log (2)+\left (1+4 x^3\right ) \log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+\left (-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5\right ) \log (2)+\left (-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5\right ) \log ^2(2)\right )+e^x \left (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+\left (5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7\right ) \log (2)+\left (507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7\right ) \log ^2(2)\right )}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+\left (-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6\right ) \log (2)+\left (-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6\right ) \log ^2(2)+e^{3 x} \left (25+10 \log (2)+\log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2+\left (-390-150 x-30 x^2\right ) \log (2)+\left (-39-15 x-3 x^2\right ) \log ^2(2)\right )+e^x \left (12675+9750 x+3825 x^2+750 x^3+75 x^4+\left (5070+3900 x+1530 x^2+300 x^3+30 x^4\right ) \log (2)+\left (507+390 x+153 x^2+30 x^3+3 x^4\right ) \log ^2(2)\right )} \, dx =\text {Too large to display} \] Input:
int((((4*x^3+1)*log(2)^2+(40*x^3+10)*log(2)+100*x^3+25)*exp(x)^3+((-12*x^5 -60*x^4-156*x^3-3*x^2-15*x-39)*log(2)^2+(-120*x^5-600*x^4-1560*x^3-30*x^2- 150*x-390)*log(2)-300*x^5-1500*x^4-3900*x^3-75*x^2-375*x-975)*exp(x)^2+((1 2*x^7+120*x^6+612*x^5+1563*x^4+2058*x^3+153*x^2+390*x+507)*log(2)^2+(120*x ^7+1200*x^6+6120*x^5+15630*x^4+20580*x^3+1530*x^2+3900*x+5070)*log(2)+300* x^7+3000*x^6+15300*x^5+39075*x^4+51450*x^3+3825*x^2+9752*x+12674)*exp(x)+( -4*x^9-60*x^8-456*x^7-2061*x^6-5943*x^5-10254*x^4-9303*x^3-1482*x^2-2535*x -2197)*log(2)^2+(-40*x^9-600*x^8-4560*x^7-20610*x^6-59430*x^5-102540*x^4-9 3030*x^3-14820*x^2-25350*x-21970)*log(2)-100*x^9-1500*x^8-11400*x^7-51525* x^6-148575*x^5-256350*x^4-232575*x^3-37053*x^2-63380*x-54912)/((log(2)^2+1 0*log(2)+25)*exp(x)^3+((-3*x^2-15*x-39)*log(2)^2+(-30*x^2-150*x-390)*log(2 )-75*x^2-375*x-975)*exp(x)^2+((3*x^4+30*x^3+153*x^2+390*x+507)*log(2)^2+(3 0*x^4+300*x^3+1530*x^2+3900*x+5070)*log(2)+75*x^4+750*x^3+3825*x^2+9750*x+ 12675)*exp(x)+(-x^6-15*x^5-114*x^4-515*x^3-1482*x^2-2535*x-2197)*log(2)^2+ (-10*x^6-150*x^5-1140*x^4-5150*x^3-14820*x^2-25350*x-21970)*log(2)-25*x^6- 375*x^5-2850*x^4-12875*x^3-37050*x^2-63375*x-54925),x)
Output:
(e**(2*x)*log(2)**2*x**4 + e**(2*x)*log(2)**2*x - 5*e**(2*x)*log(2)**2 + 1 0*e**(2*x)*log(2)*x**4 + 10*e**(2*x)*log(2)*x - 50*e**(2*x)*log(2) + 25*e* *(2*x)*x**4 + 25*e**(2*x)*x - 125*e**(2*x) - 2*e**x*log(2)**2*x**6 - 10*e* *x*log(2)**2*x**5 - 26*e**x*log(2)**2*x**4 - 2*e**x*log(2)**2*x**3 + 24*e* *x*log(2)**2*x + 130*e**x*log(2)**2 - 20*e**x*log(2)*x**6 - 100*e**x*log(2 )*x**5 - 260*e**x*log(2)*x**4 - 20*e**x*log(2)*x**3 + 240*e**x*log(2)*x + 1300*e**x*log(2) - 50*e**x*x**6 - 250*e**x*x**5 - 650*e**x*x**4 - 50*e**x* x**3 + 600*e**x*x + 3250*e**x + log(2)**2*x**8 + 10*log(2)**2*x**7 + 51*lo g(2)**2*x**6 + 131*log(2)**2*x**5 + 174*log(2)**2*x**4 + log(2)**2*x**3 - 125*log(2)**2*x**2 - 481*log(2)**2*x - 845*log(2)**2 + 10*log(2)*x**8 + 10 0*log(2)*x**7 + 510*log(2)*x**6 + 1310*log(2)*x**5 + 1740*log(2)*x**4 + 10 *log(2)*x**3 - 1250*log(2)*x**2 - 4810*log(2)*x - 8450*log(2) + 25*x**8 + 250*x**7 + 1275*x**6 + 3275*x**5 + 4350*x**4 + 25*x**3 - 3125*x**2 - 12026 *x - 21125)/(e**(2*x)*log(2)**2 + 10*e**(2*x)*log(2) + 25*e**(2*x) - 2*e** x*log(2)**2*x**2 - 10*e**x*log(2)**2*x - 26*e**x*log(2)**2 - 20*e**x*log(2 )*x**2 - 100*e**x*log(2)*x - 260*e**x*log(2) - 50*e**x*x**2 - 250*e**x*x - 650*e**x + log(2)**2*x**4 + 10*log(2)**2*x**3 + 51*log(2)**2*x**2 + 130*l og(2)**2*x + 169*log(2)**2 + 10*log(2)*x**4 + 100*log(2)*x**3 + 510*log(2) *x**2 + 1300*log(2)*x + 1690*log(2) + 25*x**4 + 250*x**3 + 1275*x**2 + 325 0*x + 4225)