Integrand size = 375, antiderivative size = 22 \[ \int \frac {36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-2330928984272-402486 x)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (-3127316274+54 x)+e^x \left (35016282+34747964 x-12 x^2\right )+\left (36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+e^x (-404558-402486 x)+2 x+e^{3 x} (-2084877534+18 x)+e^{2 x} (44998614958+3108 x)\right ) \log (x)+\left (12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^{2 x} (-347479598-6 x)+e^x (1558+1554 x)\right ) \log ^2(x)+\left (1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}+e^x (-2-2 x)\right ) \log ^3(x)+\left (-2590 e^{2 x}+30 e^{3 x}\right ) \log ^4(x)+2 e^{2 x} \log ^5(x)}{-1165463885299+67497908415 e^x-1563658110 e^{2 x}+18111870 e^{3 x}-104895 e^{4 x}+243 e^{5 x}+\left (22499302805-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}\right ) \log (x)+\left (-173739790+6037290 e^x-69930 e^{2 x}+270 e^{3 x}\right ) \log ^2(x)+\left (670810-15540 e^x+90 e^{2 x}\right ) \log ^3(x)+\left (-1295+15 e^x\right ) \log ^4(x)+\log ^5(x)} \, dx=\left (e^x-\frac {x}{\left (259-3 e^x-\log (x)\right )^2}\right )^2 \] Output:
(exp(x)-x/(259-3*exp(x)-ln(x))^2)^2
Time = 0.14 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.73 \[ \int \frac {36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-2330928984272-402486 x)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (-3127316274+54 x)+e^x \left (35016282+34747964 x-12 x^2\right )+\left (36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+e^x (-404558-402486 x)+2 x+e^{3 x} (-2084877534+18 x)+e^{2 x} (44998614958+3108 x)\right ) \log (x)+\left (12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^{2 x} (-347479598-6 x)+e^x (1558+1554 x)\right ) \log ^2(x)+\left (1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}+e^x (-2-2 x)\right ) \log ^3(x)+\left (-2590 e^{2 x}+30 e^{3 x}\right ) \log ^4(x)+2 e^{2 x} \log ^5(x)}{-1165463885299+67497908415 e^x-1563658110 e^{2 x}+18111870 e^{3 x}-104895 e^{4 x}+243 e^{5 x}+\left (22499302805-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}\right ) \log (x)+\left (-173739790+6037290 e^x-69930 e^{2 x}+270 e^{3 x}\right ) \log ^2(x)+\left (670810-15540 e^x+90 e^{2 x}\right ) \log ^3(x)+\left (-1295+15 e^x\right ) \log ^4(x)+\log ^5(x)} \, dx=e^{2 x}+\frac {x^2}{\left (-259+3 e^x+\log (x)\right )^4}-\frac {2 e^x x}{\left (-259+3 e^x+\log (x)\right )^2} \] Input:
Integrate[(36223740*E^(5*x) - 209790*E^(6*x) + 486*E^(7*x) + E^(2*x)*(-233 0928984272 - 402486*x) + E^(3*x)*(134995830852 - 4662*x) - 522*x + E^(4*x) *(-3127316274 + 54*x) + E^x*(35016282 + 34747964*x - 12*x^2) + (36223740*E ^(4*x) - 279720*E^(5*x) + 810*E^(6*x) + E^x*(-404558 - 402486*x) + 2*x + E ^(3*x)*(-2084877534 + 18*x) + E^(2*x)*(44998614958 + 3108*x))*Log[x] + (12 074580*E^(3*x) - 139860*E^(4*x) + 540*E^(5*x) + E^(2*x)*(-347479598 - 6*x) + E^x*(1558 + 1554*x))*Log[x]^2 + (1341620*E^(2*x) - 31080*E^(3*x) + 180* E^(4*x) + E^x*(-2 - 2*x))*Log[x]^3 + (-2590*E^(2*x) + 30*E^(3*x))*Log[x]^4 + 2*E^(2*x)*Log[x]^5)/(-1165463885299 + 67497908415*E^x - 1563658110*E^(2 *x) + 18111870*E^(3*x) - 104895*E^(4*x) + 243*E^(5*x) + (22499302805 - 104 2438740*E^x + 18111870*E^(2*x) - 139860*E^(3*x) + 405*E^(4*x))*Log[x] + (- 173739790 + 6037290*E^x - 69930*E^(2*x) + 270*E^(3*x))*Log[x]^2 + (670810 - 15540*E^x + 90*E^(2*x))*Log[x]^3 + (-1295 + 15*E^x)*Log[x]^4 + Log[x]^5) ,x]
Output:
E^(2*x) + x^2/(-259 + 3*E^x + Log[x])^4 - (2*E^x*x)/(-259 + 3*E^x + Log[x] )^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.
| \(\displaystyle \int \frac {e^x \left (-12 x^2+34747964 x+35016282\right )+36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-402486 x-2330928984272)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (54 x-3127316274)+2 e^{2 x} \log ^5(x)+\left (30 e^{3 x}-2590 e^{2 x}\right ) \log ^4(x)+\left (e^x (-2 x-2)+1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}\right ) \log ^3(x)+\left (e^{2 x} (-6 x-347479598)+12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^x (1554 x+1558)\right ) \log ^2(x)+\left (e^x (-402486 x-404558)+36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+2 x+e^{3 x} (18 x-2084877534)+e^{2 x} (3108 x+44998614958)\right ) \log (x)}{67497908415 e^x-1563658110 e^{2 x}+18111870 e^{3 x}-104895 e^{4 x}+243 e^{5 x}+\log ^5(x)+\left (15 e^x-1295\right ) \log ^4(x)+\left (-15540 e^x+90 e^{2 x}+670810\right ) \log ^3(x)+\left (6037290 e^x-69930 e^{2 x}+270 e^{3 x}-173739790\right ) \log ^2(x)+\left (-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}+22499302805\right ) \log (x)-1165463885299} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-e^x \left (-12 x^2+34747964 x+35016282\right )-36223740 e^{5 x}+209790 e^{6 x}-486 e^{7 x}-e^{2 x} (-402486 x-2330928984272)-e^{3 x} (134995830852-4662 x)+522 x-e^{4 x} (54 x-3127316274)-2 e^{2 x} \log ^5(x)-\left (30 e^{3 x}-2590 e^{2 x}\right ) \log ^4(x)-\left (e^x (-2 x-2)+1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}\right ) \log ^3(x)-\left (e^{2 x} (-6 x-347479598)+12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^x (1554 x+1558)\right ) \log ^2(x)-\left (e^x (-402486 x-404558)+36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+2 x+e^{3 x} (18 x-2084877534)+e^{2 x} (3108 x+44998614958)\right ) \log (x)}{\left (-3 e^x-\log (x)+259\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2 e^{2 x}+\frac {2 (x-1)}{3 \left (3 e^x+\log (x)-259\right )}+\frac {4 (\log (x)-259) (-259 x+x \log (x)-1)}{3 \left (3 e^x+\log (x)-259\right )^3}+\frac {4 x (-259 x+x \log (x)-1)}{\left (3 e^x+\log (x)-259\right )^5}-\frac {2 (-777 x+3 x \log (x)-\log (x)+257)}{3 \left (3 e^x+\log (x)-259\right )^2}-\frac {2 x (2 x-1)}{\left (3 e^x+\log (x)-259\right )^4}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -1036 \int \frac {x^2}{\left (\log (x)+3 e^x-259\right )^5}dx+4 \int \frac {x^2 \log (x)}{\left (\log (x)+3 e^x-259\right )^5}dx-4 \int \frac {x^2}{\left (\log (x)+3 e^x-259\right )^4}dx+\frac {4}{3} \int \frac {x \log ^2(x)}{\left (\log (x)+3 e^x-259\right )^3}dx-4 \int \frac {x}{\left (\log (x)+3 e^x-259\right )^5}dx+2 \int \frac {x}{\left (\log (x)+3 e^x-259\right )^4}dx+\frac {1036}{3} \int \frac {1}{\left (\log (x)+3 e^x-259\right )^3}dx+\frac {268324}{3} \int \frac {x}{\left (\log (x)+3 e^x-259\right )^3}dx-\frac {4}{3} \int \frac {\log (x)}{\left (\log (x)+3 e^x-259\right )^3}dx-\frac {2072}{3} \int \frac {x \log (x)}{\left (\log (x)+3 e^x-259\right )^3}dx-\frac {514}{3} \int \frac {1}{\left (\log (x)+3 e^x-259\right )^2}dx+518 \int \frac {x}{\left (\log (x)+3 e^x-259\right )^2}dx+\frac {2}{3} \int \frac {\log (x)}{\left (\log (x)+3 e^x-259\right )^2}dx-2 \int \frac {x \log (x)}{\left (\log (x)+3 e^x-259\right )^2}dx-\frac {2}{3} \int \frac {1}{\log (x)+3 e^x-259}dx+\frac {2}{3} \int \frac {x}{\log (x)+3 e^x-259}dx+e^{2 x}\) |
Input:
Int[(36223740*E^(5*x) - 209790*E^(6*x) + 486*E^(7*x) + E^(2*x)*(-233092898 4272 - 402486*x) + E^(3*x)*(134995830852 - 4662*x) - 522*x + E^(4*x)*(-312 7316274 + 54*x) + E^x*(35016282 + 34747964*x - 12*x^2) + (36223740*E^(4*x) - 279720*E^(5*x) + 810*E^(6*x) + E^x*(-404558 - 402486*x) + 2*x + E^(3*x) *(-2084877534 + 18*x) + E^(2*x)*(44998614958 + 3108*x))*Log[x] + (12074580 *E^(3*x) - 139860*E^(4*x) + 540*E^(5*x) + E^(2*x)*(-347479598 - 6*x) + E^x *(1558 + 1554*x))*Log[x]^2 + (1341620*E^(2*x) - 31080*E^(3*x) + 180*E^(4*x ) + E^x*(-2 - 2*x))*Log[x]^3 + (-2590*E^(2*x) + 30*E^(3*x))*Log[x]^4 + 2*E ^(2*x)*Log[x]^5)/(-1165463885299 + 67497908415*E^x - 1563658110*E^(2*x) + 18111870*E^(3*x) - 104895*E^(4*x) + 243*E^(5*x) + (22499302805 - 104243874 0*E^x + 18111870*E^(2*x) - 139860*E^(3*x) + 405*E^(4*x))*Log[x] + (-173739 790 + 6037290*E^x - 69930*E^(2*x) + 270*E^(3*x))*Log[x]^2 + (670810 - 1554 0*E^x + 90*E^(2*x))*Log[x]^3 + (-1295 + 15*E^x)*Log[x]^4 + Log[x]^5),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs. \(2(20)=40\).
Time = 0.05 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.64
\[{\mathrm e}^{2 x}+\frac {x \left (-18 \,{\mathrm e}^{3 x}-12 \,{\mathrm e}^{2 x} \ln \left (x \right )-2 \,{\mathrm e}^{x} \ln \left (x \right )^{2}+3108 \,{\mathrm e}^{2 x}+1036 \,{\mathrm e}^{x} \ln \left (x \right )+x -134162 \,{\mathrm e}^{x}\right )}{\left (3 \,{\mathrm e}^{x}+\ln \left (x \right )-259\right )^{4}}\]
Input:
int((2*exp(x)^2*ln(x)^5+(30*exp(x)^3-2590*exp(x)^2)*ln(x)^4+(180*exp(x)^4- 31080*exp(x)^3+1341620*exp(x)^2+(-2-2*x)*exp(x))*ln(x)^3+(540*exp(x)^5-139 860*exp(x)^4+12074580*exp(x)^3+(-6*x-347479598)*exp(x)^2+(1554*x+1558)*exp (x))*ln(x)^2+(810*exp(x)^6-279720*exp(x)^5+36223740*exp(x)^4+(18*x-2084877 534)*exp(x)^3+(3108*x+44998614958)*exp(x)^2+(-402486*x-404558)*exp(x)+2*x) *ln(x)+486*exp(x)^7-209790*exp(x)^6+36223740*exp(x)^5+(54*x-3127316274)*ex p(x)^4+(-4662*x+134995830852)*exp(x)^3+(-402486*x-2330928984272)*exp(x)^2+ (-12*x^2+34747964*x+35016282)*exp(x)-522*x)/(ln(x)^5+(15*exp(x)-1295)*ln(x )^4+(90*exp(x)^2-15540*exp(x)+670810)*ln(x)^3+(270*exp(x)^3-69930*exp(x)^2 +6037290*exp(x)-173739790)*ln(x)^2+(405*exp(x)^4-139860*exp(x)^3+18111870* exp(x)^2-1042438740*exp(x)+22499302805)*ln(x)+243*exp(x)^5-104895*exp(x)^4 +18111870*exp(x)^3-1563658110*exp(x)^2+67497908415*exp(x)-1165463885299),x )
Output:
exp(x)^2+x*(-18*exp(x)^3-12*exp(x)^2*ln(x)-2*exp(x)*ln(x)^2+3108*exp(x)^2+ 1036*exp(x)*ln(x)+x-134162*exp(x))/(3*exp(x)+ln(x)-259)^4
Leaf count of result is larger than twice the leaf count of optimal. 227 vs. \(2 (19) = 38\).
Time = 0.11 (sec) , antiderivative size = 227, normalized size of antiderivative = 10.32 \[ \int \frac {36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-2330928984272-402486 x)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (-3127316274+54 x)+e^x \left (35016282+34747964 x-12 x^2\right )+\left (36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+e^x (-404558-402486 x)+2 x+e^{3 x} (-2084877534+18 x)+e^{2 x} (44998614958+3108 x)\right ) \log (x)+\left (12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^{2 x} (-347479598-6 x)+e^x (1558+1554 x)\right ) \log ^2(x)+\left (1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}+e^x (-2-2 x)\right ) \log ^3(x)+\left (-2590 e^{2 x}+30 e^{3 x}\right ) \log ^4(x)+2 e^{2 x} \log ^5(x)}{-1165463885299+67497908415 e^x-1563658110 e^{2 x}+18111870 e^{3 x}-104895 e^{4 x}+243 e^{5 x}+\left (22499302805-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}\right ) \log (x)+\left (-173739790+6037290 e^x-69930 e^{2 x}+270 e^{3 x}\right ) \log ^2(x)+\left (670810-15540 e^x+90 e^{2 x}\right ) \log ^3(x)+\left (-1295+15 e^x\right ) \log ^4(x)+\log ^5(x)} \, dx=\frac {e^{\left (2 \, x\right )} \log \left (x\right )^{4} + 4 \, {\left (3 \, e^{\left (3 \, x\right )} - 259 \, e^{\left (2 \, x\right )}\right )} \log \left (x\right )^{3} - 2 \, {\left (x e^{x} - 27 \, e^{\left (4 \, x\right )} + 4662 \, e^{\left (3 \, x\right )} - 201243 \, e^{\left (2 \, x\right )}\right )} \log \left (x\right )^{2} + x^{2} - 6 \, {\left (3 \, x + 34747958\right )} e^{\left (3 \, x\right )} + 259 \, {\left (12 \, x + 17373979\right )} e^{\left (2 \, x\right )} - 134162 \, x e^{x} - 4 \, {\left ({\left (3 \, x + 17373979\right )} e^{\left (2 \, x\right )} - 259 \, x e^{x} - 27 \, e^{\left (5 \, x\right )} + 6993 \, e^{\left (4 \, x\right )} - 603729 \, e^{\left (3 \, x\right )}\right )} \log \left (x\right ) + 81 \, e^{\left (6 \, x\right )} - 27972 \, e^{\left (5 \, x\right )} + 3622374 \, e^{\left (4 \, x\right )}}{4 \, {\left (3 \, e^{x} - 259\right )} \log \left (x\right )^{3} + \log \left (x\right )^{4} + 6 \, {\left (9 \, e^{\left (2 \, x\right )} - 1554 \, e^{x} + 67081\right )} \log \left (x\right )^{2} + 4 \, {\left (27 \, e^{\left (3 \, x\right )} - 6993 \, e^{\left (2 \, x\right )} + 603729 \, e^{x} - 17373979\right )} \log \left (x\right ) + 81 \, e^{\left (4 \, x\right )} - 27972 \, e^{\left (3 \, x\right )} + 3622374 \, e^{\left (2 \, x\right )} - 208487748 \, e^{x} + 4499860561} \] Input:
integrate((2*exp(x)^2*log(x)^5+(30*exp(x)^3-2590*exp(x)^2)*log(x)^4+(180*e xp(x)^4-31080*exp(x)^3+1341620*exp(x)^2+(-2-2*x)*exp(x))*log(x)^3+(540*exp (x)^5-139860*exp(x)^4+12074580*exp(x)^3+(-6*x-347479598)*exp(x)^2+(1554*x+ 1558)*exp(x))*log(x)^2+(810*exp(x)^6-279720*exp(x)^5+36223740*exp(x)^4+(18 *x-2084877534)*exp(x)^3+(3108*x+44998614958)*exp(x)^2+(-402486*x-404558)*e xp(x)+2*x)*log(x)+486*exp(x)^7-209790*exp(x)^6+36223740*exp(x)^5+(54*x-312 7316274)*exp(x)^4+(-4662*x+134995830852)*exp(x)^3+(-402486*x-2330928984272 )*exp(x)^2+(-12*x^2+34747964*x+35016282)*exp(x)-522*x)/(log(x)^5+(15*exp(x )-1295)*log(x)^4+(90*exp(x)^2-15540*exp(x)+670810)*log(x)^3+(270*exp(x)^3- 69930*exp(x)^2+6037290*exp(x)-173739790)*log(x)^2+(405*exp(x)^4-139860*exp (x)^3+18111870*exp(x)^2-1042438740*exp(x)+22499302805)*log(x)+243*exp(x)^5 -104895*exp(x)^4+18111870*exp(x)^3-1563658110*exp(x)^2+67497908415*exp(x)- 1165463885299),x, algorithm="fricas")
Output:
(e^(2*x)*log(x)^4 + 4*(3*e^(3*x) - 259*e^(2*x))*log(x)^3 - 2*(x*e^x - 27*e ^(4*x) + 4662*e^(3*x) - 201243*e^(2*x))*log(x)^2 + x^2 - 6*(3*x + 34747958 )*e^(3*x) + 259*(12*x + 17373979)*e^(2*x) - 134162*x*e^x - 4*((3*x + 17373 979)*e^(2*x) - 259*x*e^x - 27*e^(5*x) + 6993*e^(4*x) - 603729*e^(3*x))*log (x) + 81*e^(6*x) - 27972*e^(5*x) + 3622374*e^(4*x))/(4*(3*e^x - 259)*log(x )^3 + log(x)^4 + 6*(9*e^(2*x) - 1554*e^x + 67081)*log(x)^2 + 4*(27*e^(3*x) - 6993*e^(2*x) + 603729*e^x - 17373979)*log(x) + 81*e^(4*x) - 27972*e^(3* x) + 3622374*e^(2*x) - 208487748*e^x + 4499860561)
Leaf count of result is larger than twice the leaf count of optimal. 139 vs. \(2 (17) = 34\).
Time = 0.34 (sec) , antiderivative size = 139, normalized size of antiderivative = 6.32 \[ \int \frac {36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-2330928984272-402486 x)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (-3127316274+54 x)+e^x \left (35016282+34747964 x-12 x^2\right )+\left (36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+e^x (-404558-402486 x)+2 x+e^{3 x} (-2084877534+18 x)+e^{2 x} (44998614958+3108 x)\right ) \log (x)+\left (12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^{2 x} (-347479598-6 x)+e^x (1558+1554 x)\right ) \log ^2(x)+\left (1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}+e^x (-2-2 x)\right ) \log ^3(x)+\left (-2590 e^{2 x}+30 e^{3 x}\right ) \log ^4(x)+2 e^{2 x} \log ^5(x)}{-1165463885299+67497908415 e^x-1563658110 e^{2 x}+18111870 e^{3 x}-104895 e^{4 x}+243 e^{5 x}+\left (22499302805-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}\right ) \log (x)+\left (-173739790+6037290 e^x-69930 e^{2 x}+270 e^{3 x}\right ) \log ^2(x)+\left (670810-15540 e^x+90 e^{2 x}\right ) \log ^3(x)+\left (-1295+15 e^x\right ) \log ^4(x)+\log ^5(x)} \, dx=\frac {x^{2} - 18 x e^{3 x} + \left (- 12 x \log {\left (x \right )} + 3108 x\right ) e^{2 x} + \left (- 2 x \log {\left (x \right )}^{2} + 1036 x \log {\left (x \right )} - 134162 x\right ) e^{x}}{\left (108 \log {\left (x \right )} - 27972\right ) e^{3 x} + \left (54 \log {\left (x \right )}^{2} - 27972 \log {\left (x \right )} + 3622374\right ) e^{2 x} + \left (12 \log {\left (x \right )}^{3} - 9324 \log {\left (x \right )}^{2} + 2414916 \log {\left (x \right )} - 208487748\right ) e^{x} + 81 e^{4 x} + \log {\left (x \right )}^{4} - 1036 \log {\left (x \right )}^{3} + 402486 \log {\left (x \right )}^{2} - 69495916 \log {\left (x \right )} + 4499860561} + e^{2 x} \] Input:
integrate((2*exp(x)**2*ln(x)**5+(30*exp(x)**3-2590*exp(x)**2)*ln(x)**4+(18 0*exp(x)**4-31080*exp(x)**3+1341620*exp(x)**2+(-2-2*x)*exp(x))*ln(x)**3+(5 40*exp(x)**5-139860*exp(x)**4+12074580*exp(x)**3+(-6*x-347479598)*exp(x)** 2+(1554*x+1558)*exp(x))*ln(x)**2+(810*exp(x)**6-279720*exp(x)**5+36223740* exp(x)**4+(18*x-2084877534)*exp(x)**3+(3108*x+44998614958)*exp(x)**2+(-402 486*x-404558)*exp(x)+2*x)*ln(x)+486*exp(x)**7-209790*exp(x)**6+36223740*ex p(x)**5+(54*x-3127316274)*exp(x)**4+(-4662*x+134995830852)*exp(x)**3+(-402 486*x-2330928984272)*exp(x)**2+(-12*x**2+34747964*x+35016282)*exp(x)-522*x )/(ln(x)**5+(15*exp(x)-1295)*ln(x)**4+(90*exp(x)**2-15540*exp(x)+670810)*l n(x)**3+(270*exp(x)**3-69930*exp(x)**2+6037290*exp(x)-173739790)*ln(x)**2+ (405*exp(x)**4-139860*exp(x)**3+18111870*exp(x)**2-1042438740*exp(x)+22499 302805)*ln(x)+243*exp(x)**5-104895*exp(x)**4+18111870*exp(x)**3-1563658110 *exp(x)**2+67497908415*exp(x)-1165463885299),x)
Output:
(x**2 - 18*x*exp(3*x) + (-12*x*log(x) + 3108*x)*exp(2*x) + (-2*x*log(x)**2 + 1036*x*log(x) - 134162*x)*exp(x))/((108*log(x) - 27972)*exp(3*x) + (54* log(x)**2 - 27972*log(x) + 3622374)*exp(2*x) + (12*log(x)**3 - 9324*log(x) **2 + 2414916*log(x) - 208487748)*exp(x) + 81*exp(4*x) + log(x)**4 - 1036* log(x)**3 + 402486*log(x)**2 - 69495916*log(x) + 4499860561) + exp(2*x)
Leaf count of result is larger than twice the leaf count of optimal. 194 vs. \(2 (19) = 38\).
Time = 0.48 (sec) , antiderivative size = 194, normalized size of antiderivative = 8.82 \[ \int \frac {36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-2330928984272-402486 x)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (-3127316274+54 x)+e^x \left (35016282+34747964 x-12 x^2\right )+\left (36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+e^x (-404558-402486 x)+2 x+e^{3 x} (-2084877534+18 x)+e^{2 x} (44998614958+3108 x)\right ) \log (x)+\left (12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^{2 x} (-347479598-6 x)+e^x (1558+1554 x)\right ) \log ^2(x)+\left (1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}+e^x (-2-2 x)\right ) \log ^3(x)+\left (-2590 e^{2 x}+30 e^{3 x}\right ) \log ^4(x)+2 e^{2 x} \log ^5(x)}{-1165463885299+67497908415 e^x-1563658110 e^{2 x}+18111870 e^{3 x}-104895 e^{4 x}+243 e^{5 x}+\left (22499302805-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}\right ) \log (x)+\left (-173739790+6037290 e^x-69930 e^{2 x}+270 e^{3 x}\right ) \log ^2(x)+\left (670810-15540 e^x+90 e^{2 x}\right ) \log ^3(x)+\left (-1295+15 e^x\right ) \log ^4(x)+\log ^5(x)} \, dx=\frac {x^{2} + 108 \, {\left (\log \left (x\right ) - 259\right )} e^{\left (5 \, x\right )} + 54 \, {\left (\log \left (x\right )^{2} - 518 \, \log \left (x\right ) + 67081\right )} e^{\left (4 \, x\right )} + 6 \, {\left (2 \, \log \left (x\right )^{3} - 1554 \, \log \left (x\right )^{2} - 3 \, x + 402486 \, \log \left (x\right ) - 34747958\right )} e^{\left (3 \, x\right )} + {\left (\log \left (x\right )^{4} - 1036 \, \log \left (x\right )^{3} - 4 \, {\left (3 \, x + 17373979\right )} \log \left (x\right ) + 402486 \, \log \left (x\right )^{2} + 3108 \, x + 4499860561\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x \log \left (x\right )^{2} - 518 \, x \log \left (x\right ) + 67081 \, x\right )} e^{x} + 81 \, e^{\left (6 \, x\right )}}{\log \left (x\right )^{4} - 1036 \, \log \left (x\right )^{3} + 108 \, {\left (\log \left (x\right ) - 259\right )} e^{\left (3 \, x\right )} + 54 \, {\left (\log \left (x\right )^{2} - 518 \, \log \left (x\right ) + 67081\right )} e^{\left (2 \, x\right )} + 12 \, {\left (\log \left (x\right )^{3} - 777 \, \log \left (x\right )^{2} + 201243 \, \log \left (x\right ) - 17373979\right )} e^{x} + 402486 \, \log \left (x\right )^{2} + 81 \, e^{\left (4 \, x\right )} - 69495916 \, \log \left (x\right ) + 4499860561} \] Input:
integrate((2*exp(x)^2*log(x)^5+(30*exp(x)^3-2590*exp(x)^2)*log(x)^4+(180*e xp(x)^4-31080*exp(x)^3+1341620*exp(x)^2+(-2-2*x)*exp(x))*log(x)^3+(540*exp (x)^5-139860*exp(x)^4+12074580*exp(x)^3+(-6*x-347479598)*exp(x)^2+(1554*x+ 1558)*exp(x))*log(x)^2+(810*exp(x)^6-279720*exp(x)^5+36223740*exp(x)^4+(18 *x-2084877534)*exp(x)^3+(3108*x+44998614958)*exp(x)^2+(-402486*x-404558)*e xp(x)+2*x)*log(x)+486*exp(x)^7-209790*exp(x)^6+36223740*exp(x)^5+(54*x-312 7316274)*exp(x)^4+(-4662*x+134995830852)*exp(x)^3+(-402486*x-2330928984272 )*exp(x)^2+(-12*x^2+34747964*x+35016282)*exp(x)-522*x)/(log(x)^5+(15*exp(x )-1295)*log(x)^4+(90*exp(x)^2-15540*exp(x)+670810)*log(x)^3+(270*exp(x)^3- 69930*exp(x)^2+6037290*exp(x)-173739790)*log(x)^2+(405*exp(x)^4-139860*exp (x)^3+18111870*exp(x)^2-1042438740*exp(x)+22499302805)*log(x)+243*exp(x)^5 -104895*exp(x)^4+18111870*exp(x)^3-1563658110*exp(x)^2+67497908415*exp(x)- 1165463885299),x, algorithm="maxima")
Output:
(x^2 + 108*(log(x) - 259)*e^(5*x) + 54*(log(x)^2 - 518*log(x) + 67081)*e^( 4*x) + 6*(2*log(x)^3 - 1554*log(x)^2 - 3*x + 402486*log(x) - 34747958)*e^( 3*x) + (log(x)^4 - 1036*log(x)^3 - 4*(3*x + 17373979)*log(x) + 402486*log( x)^2 + 3108*x + 4499860561)*e^(2*x) - 2*(x*log(x)^2 - 518*x*log(x) + 67081 *x)*e^x + 81*e^(6*x))/(log(x)^4 - 1036*log(x)^3 + 108*(log(x) - 259)*e^(3* x) + 54*(log(x)^2 - 518*log(x) + 67081)*e^(2*x) + 12*(log(x)^3 - 777*log(x )^2 + 201243*log(x) - 17373979)*e^x + 402486*log(x)^2 + 81*e^(4*x) - 69495 916*log(x) + 4499860561)
Leaf count of result is larger than twice the leaf count of optimal. 264 vs. \(2 (19) = 38\).
Time = 0.60 (sec) , antiderivative size = 264, normalized size of antiderivative = 12.00 \[ \int \frac {36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-2330928984272-402486 x)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (-3127316274+54 x)+e^x \left (35016282+34747964 x-12 x^2\right )+\left (36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+e^x (-404558-402486 x)+2 x+e^{3 x} (-2084877534+18 x)+e^{2 x} (44998614958+3108 x)\right ) \log (x)+\left (12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^{2 x} (-347479598-6 x)+e^x (1558+1554 x)\right ) \log ^2(x)+\left (1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}+e^x (-2-2 x)\right ) \log ^3(x)+\left (-2590 e^{2 x}+30 e^{3 x}\right ) \log ^4(x)+2 e^{2 x} \log ^5(x)}{-1165463885299+67497908415 e^x-1563658110 e^{2 x}+18111870 e^{3 x}-104895 e^{4 x}+243 e^{5 x}+\left (22499302805-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}\right ) \log (x)+\left (-173739790+6037290 e^x-69930 e^{2 x}+270 e^{3 x}\right ) \log ^2(x)+\left (670810-15540 e^x+90 e^{2 x}\right ) \log ^3(x)+\left (-1295+15 e^x\right ) \log ^4(x)+\log ^5(x)} \, dx=\frac {e^{\left (2 \, x\right )} \log \left (x\right )^{4} - 2 \, x e^{x} \log \left (x\right )^{2} + 12 \, e^{\left (3 \, x\right )} \log \left (x\right )^{3} - 1036 \, e^{\left (2 \, x\right )} \log \left (x\right )^{3} - 12 \, x e^{\left (2 \, x\right )} \log \left (x\right ) + 1036 \, x e^{x} \log \left (x\right ) + 54 \, e^{\left (4 \, x\right )} \log \left (x\right )^{2} - 9324 \, e^{\left (3 \, x\right )} \log \left (x\right )^{2} + 402486 \, e^{\left (2 \, x\right )} \log \left (x\right )^{2} + x^{2} - 18 \, x e^{\left (3 \, x\right )} + 3108 \, x e^{\left (2 \, x\right )} - 134162 \, x e^{x} + 108 \, e^{\left (5 \, x\right )} \log \left (x\right ) - 27972 \, e^{\left (4 \, x\right )} \log \left (x\right ) + 2414916 \, e^{\left (3 \, x\right )} \log \left (x\right ) - 69495916 \, e^{\left (2 \, x\right )} \log \left (x\right ) + 81 \, e^{\left (6 \, x\right )} - 27972 \, e^{\left (5 \, x\right )} + 3622374 \, e^{\left (4 \, x\right )} - 208487748 \, e^{\left (3 \, x\right )} + 4499860561 \, e^{\left (2 \, x\right )}}{12 \, e^{x} \log \left (x\right )^{3} + \log \left (x\right )^{4} + 54 \, e^{\left (2 \, x\right )} \log \left (x\right )^{2} - 9324 \, e^{x} \log \left (x\right )^{2} - 1036 \, \log \left (x\right )^{3} + 108 \, e^{\left (3 \, x\right )} \log \left (x\right ) - 27972 \, e^{\left (2 \, x\right )} \log \left (x\right ) + 2414916 \, e^{x} \log \left (x\right ) + 402486 \, \log \left (x\right )^{2} + 81 \, e^{\left (4 \, x\right )} - 27972 \, e^{\left (3 \, x\right )} + 3622374 \, e^{\left (2 \, x\right )} - 208487748 \, e^{x} - 69495916 \, \log \left (x\right ) + 4499860561} \] Input:
integrate((2*exp(x)^2*log(x)^5+(30*exp(x)^3-2590*exp(x)^2)*log(x)^4+(180*e xp(x)^4-31080*exp(x)^3+1341620*exp(x)^2+(-2-2*x)*exp(x))*log(x)^3+(540*exp (x)^5-139860*exp(x)^4+12074580*exp(x)^3+(-6*x-347479598)*exp(x)^2+(1554*x+ 1558)*exp(x))*log(x)^2+(810*exp(x)^6-279720*exp(x)^5+36223740*exp(x)^4+(18 *x-2084877534)*exp(x)^3+(3108*x+44998614958)*exp(x)^2+(-402486*x-404558)*e xp(x)+2*x)*log(x)+486*exp(x)^7-209790*exp(x)^6+36223740*exp(x)^5+(54*x-312 7316274)*exp(x)^4+(-4662*x+134995830852)*exp(x)^3+(-402486*x-2330928984272 )*exp(x)^2+(-12*x^2+34747964*x+35016282)*exp(x)-522*x)/(log(x)^5+(15*exp(x )-1295)*log(x)^4+(90*exp(x)^2-15540*exp(x)+670810)*log(x)^3+(270*exp(x)^3- 69930*exp(x)^2+6037290*exp(x)-173739790)*log(x)^2+(405*exp(x)^4-139860*exp (x)^3+18111870*exp(x)^2-1042438740*exp(x)+22499302805)*log(x)+243*exp(x)^5 -104895*exp(x)^4+18111870*exp(x)^3-1563658110*exp(x)^2+67497908415*exp(x)- 1165463885299),x, algorithm="giac")
Output:
(e^(2*x)*log(x)^4 - 2*x*e^x*log(x)^2 + 12*e^(3*x)*log(x)^3 - 1036*e^(2*x)* log(x)^3 - 12*x*e^(2*x)*log(x) + 1036*x*e^x*log(x) + 54*e^(4*x)*log(x)^2 - 9324*e^(3*x)*log(x)^2 + 402486*e^(2*x)*log(x)^2 + x^2 - 18*x*e^(3*x) + 31 08*x*e^(2*x) - 134162*x*e^x + 108*e^(5*x)*log(x) - 27972*e^(4*x)*log(x) + 2414916*e^(3*x)*log(x) - 69495916*e^(2*x)*log(x) + 81*e^(6*x) - 27972*e^(5 *x) + 3622374*e^(4*x) - 208487748*e^(3*x) + 4499860561*e^(2*x))/(12*e^x*lo g(x)^3 + log(x)^4 + 54*e^(2*x)*log(x)^2 - 9324*e^x*log(x)^2 - 1036*log(x)^ 3 + 108*e^(3*x)*log(x) - 27972*e^(2*x)*log(x) + 2414916*e^x*log(x) + 40248 6*log(x)^2 + 81*e^(4*x) - 27972*e^(3*x) + 3622374*e^(2*x) - 208487748*e^x - 69495916*log(x) + 4499860561)
Timed out. \[ \int \frac {36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-2330928984272-402486 x)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (-3127316274+54 x)+e^x \left (35016282+34747964 x-12 x^2\right )+\left (36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+e^x (-404558-402486 x)+2 x+e^{3 x} (-2084877534+18 x)+e^{2 x} (44998614958+3108 x)\right ) \log (x)+\left (12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^{2 x} (-347479598-6 x)+e^x (1558+1554 x)\right ) \log ^2(x)+\left (1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}+e^x (-2-2 x)\right ) \log ^3(x)+\left (-2590 e^{2 x}+30 e^{3 x}\right ) \log ^4(x)+2 e^{2 x} \log ^5(x)}{-1165463885299+67497908415 e^x-1563658110 e^{2 x}+18111870 e^{3 x}-104895 e^{4 x}+243 e^{5 x}+\left (22499302805-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}\right ) \log (x)+\left (-173739790+6037290 e^x-69930 e^{2 x}+270 e^{3 x}\right ) \log ^2(x)+\left (670810-15540 e^x+90 e^{2 x}\right ) \log ^3(x)+\left (-1295+15 e^x\right ) \log ^4(x)+\log ^5(x)} \, dx=\int \frac {2\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^5+\left (30\,{\mathrm {e}}^{3\,x}-2590\,{\mathrm {e}}^{2\,x}\right )\,{\ln \left (x\right )}^4+\left (1341620\,{\mathrm {e}}^{2\,x}-31080\,{\mathrm {e}}^{3\,x}+180\,{\mathrm {e}}^{4\,x}-{\mathrm {e}}^x\,\left (2\,x+2\right )\right )\,{\ln \left (x\right )}^3+\left (12074580\,{\mathrm {e}}^{3\,x}-139860\,{\mathrm {e}}^{4\,x}+540\,{\mathrm {e}}^{5\,x}+{\mathrm {e}}^x\,\left (1554\,x+1558\right )-{\mathrm {e}}^{2\,x}\,\left (6\,x+347479598\right )\right )\,{\ln \left (x\right )}^2+\left (2\,x+36223740\,{\mathrm {e}}^{4\,x}-279720\,{\mathrm {e}}^{5\,x}+810\,{\mathrm {e}}^{6\,x}+{\mathrm {e}}^{2\,x}\,\left (3108\,x+44998614958\right )+{\mathrm {e}}^{3\,x}\,\left (18\,x-2084877534\right )-{\mathrm {e}}^x\,\left (402486\,x+404558\right )\right )\,\ln \left (x\right )-522\,x+36223740\,{\mathrm {e}}^{5\,x}-209790\,{\mathrm {e}}^{6\,x}+486\,{\mathrm {e}}^{7\,x}-{\mathrm {e}}^{3\,x}\,\left (4662\,x-134995830852\right )-{\mathrm {e}}^{2\,x}\,\left (402486\,x+2330928984272\right )+{\mathrm {e}}^{4\,x}\,\left (54\,x-3127316274\right )+{\mathrm {e}}^x\,\left (-12\,x^2+34747964\,x+35016282\right )}{{\ln \left (x\right )}^5+\left (15\,{\mathrm {e}}^x-1295\right )\,{\ln \left (x\right )}^4+\left (90\,{\mathrm {e}}^{2\,x}-15540\,{\mathrm {e}}^x+670810\right )\,{\ln \left (x\right )}^3+\left (270\,{\mathrm {e}}^{3\,x}-69930\,{\mathrm {e}}^{2\,x}+6037290\,{\mathrm {e}}^x-173739790\right )\,{\ln \left (x\right )}^2+\left (18111870\,{\mathrm {e}}^{2\,x}-139860\,{\mathrm {e}}^{3\,x}+405\,{\mathrm {e}}^{4\,x}-1042438740\,{\mathrm {e}}^x+22499302805\right )\,\ln \left (x\right )-1563658110\,{\mathrm {e}}^{2\,x}+18111870\,{\mathrm {e}}^{3\,x}-104895\,{\mathrm {e}}^{4\,x}+243\,{\mathrm {e}}^{5\,x}+67497908415\,{\mathrm {e}}^x-1165463885299} \,d x \] Input:
int((36223740*exp(5*x) - 522*x - 209790*exp(6*x) + 486*exp(7*x) + log(x)^2 *(12074580*exp(3*x) - 139860*exp(4*x) + 540*exp(5*x) + exp(x)*(1554*x + 15 58) - exp(2*x)*(6*x + 347479598)) - log(x)^4*(2590*exp(2*x) - 30*exp(3*x)) - exp(3*x)*(4662*x - 134995830852) + log(x)^3*(1341620*exp(2*x) - 31080*e xp(3*x) + 180*exp(4*x) - exp(x)*(2*x + 2)) + log(x)*(2*x + 36223740*exp(4* x) - 279720*exp(5*x) + 810*exp(6*x) + exp(2*x)*(3108*x + 44998614958) + ex p(3*x)*(18*x - 2084877534) - exp(x)*(402486*x + 404558)) - exp(2*x)*(40248 6*x + 2330928984272) + exp(4*x)*(54*x - 3127316274) + exp(x)*(34747964*x - 12*x^2 + 35016282) + 2*exp(2*x)*log(x)^5)/(18111870*exp(3*x) - 1563658110 *exp(2*x) - 104895*exp(4*x) + 243*exp(5*x) + 67497908415*exp(x) + log(x)*( 18111870*exp(2*x) - 139860*exp(3*x) + 405*exp(4*x) - 1042438740*exp(x) + 2 2499302805) + log(x)^4*(15*exp(x) - 1295) + log(x)^5 - log(x)^2*(69930*exp (2*x) - 270*exp(3*x) - 6037290*exp(x) + 173739790) + log(x)^3*(90*exp(2*x) - 15540*exp(x) + 670810) - 1165463885299),x)
Output:
int((36223740*exp(5*x) - 522*x - 209790*exp(6*x) + 486*exp(7*x) + log(x)^2 *(12074580*exp(3*x) - 139860*exp(4*x) + 540*exp(5*x) + exp(x)*(1554*x + 15 58) - exp(2*x)*(6*x + 347479598)) - log(x)^4*(2590*exp(2*x) - 30*exp(3*x)) - exp(3*x)*(4662*x - 134995830852) + log(x)^3*(1341620*exp(2*x) - 31080*e xp(3*x) + 180*exp(4*x) - exp(x)*(2*x + 2)) + log(x)*(2*x + 36223740*exp(4* x) - 279720*exp(5*x) + 810*exp(6*x) + exp(2*x)*(3108*x + 44998614958) + ex p(3*x)*(18*x - 2084877534) - exp(x)*(402486*x + 404558)) - exp(2*x)*(40248 6*x + 2330928984272) + exp(4*x)*(54*x - 3127316274) + exp(x)*(34747964*x - 12*x^2 + 35016282) + 2*exp(2*x)*log(x)^5)/(18111870*exp(3*x) - 1563658110 *exp(2*x) - 104895*exp(4*x) + 243*exp(5*x) + 67497908415*exp(x) + log(x)*( 18111870*exp(2*x) - 139860*exp(3*x) + 405*exp(4*x) - 1042438740*exp(x) + 2 2499302805) + log(x)^4*(15*exp(x) - 1295) + log(x)^5 - log(x)^2*(69930*exp (2*x) - 270*exp(3*x) - 6037290*exp(x) + 173739790) + log(x)^3*(90*exp(2*x) - 15540*exp(x) + 670810) - 1165463885299), x)
Time = 0.18 (sec) , antiderivative size = 344, normalized size of antiderivative = 15.64 \[ \int \frac {36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-2330928984272-402486 x)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (-3127316274+54 x)+e^x \left (35016282+34747964 x-12 x^2\right )+\left (36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+e^x (-404558-402486 x)+2 x+e^{3 x} (-2084877534+18 x)+e^{2 x} (44998614958+3108 x)\right ) \log (x)+\left (12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^{2 x} (-347479598-6 x)+e^x (1558+1554 x)\right ) \log ^2(x)+\left (1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}+e^x (-2-2 x)\right ) \log ^3(x)+\left (-2590 e^{2 x}+30 e^{3 x}\right ) \log ^4(x)+2 e^{2 x} \log ^5(x)}{-1165463885299+67497908415 e^x-1563658110 e^{2 x}+18111870 e^{3 x}-104895 e^{4 x}+243 e^{5 x}+\left (22499302805-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}\right ) \log (x)+\left (-173739790+6037290 e^x-69930 e^{2 x}+270 e^{3 x}\right ) \log ^2(x)+\left (670810-15540 e^x+90 e^{2 x}\right ) \log ^3(x)+\left (-1295+15 e^x\right ) \log ^4(x)+\log ^5(x)} \, dx=\frac {-301855146292441-161994980196 e^{x} \mathrm {log}\left (x \right )-83916 e^{5 x}-6 e^{x} \mathrm {log}\left (x \right )^{2} x +3 x^{2}-36 e^{2 x} \mathrm {log}\left (x \right ) x -54 e^{3 x} x +4661855541196 \,\mathrm {log}\left (x \right )+9324 e^{2 x} x +13985566623588 e^{x}-229492888611 e^{2 x}-67081 \mathrm {log}\left (x \right )^{4}+324 e^{5 x} \mathrm {log}\left (x \right )+162 e^{4 x} \mathrm {log}\left (x \right )^{2}+36 e^{3 x} \mathrm {log}\left (x \right )^{3}-27972 e^{3 x} \mathrm {log}\left (x \right )^{2}+3 e^{2 x} \mathrm {log}\left (x \right )^{4}-3108 e^{2 x} \mathrm {log}\left (x \right )^{3}-2414916 e^{2 x} \mathrm {log}\left (x \right )^{2}+1667901984 e^{2 x} \mathrm {log}\left (x \right )-804972 e^{x} \mathrm {log}\left (x \right )^{3}-26999163366 \mathrm {log}\left (x \right )^{2}+3108 e^{x} \mathrm {log}\left (x \right ) x +243 e^{6 x}+5433561 e^{4 x}+1250926488 e^{3 x}-83916 e^{4 x} \mathrm {log}\left (x \right )+625463244 e^{x} \mathrm {log}\left (x \right )^{2}-402486 e^{x} x +69495916 \mathrm {log}\left (x \right )^{3}}{243 e^{4 x}+324 e^{3 x} \mathrm {log}\left (x \right )-83916 e^{3 x}+162 e^{2 x} \mathrm {log}\left (x \right )^{2}-83916 e^{2 x} \mathrm {log}\left (x \right )+10867122 e^{2 x}+36 e^{x} \mathrm {log}\left (x \right )^{3}-27972 e^{x} \mathrm {log}\left (x \right )^{2}+7244748 e^{x} \mathrm {log}\left (x \right )-625463244 e^{x}+3 \mathrm {log}\left (x \right )^{4}-3108 \mathrm {log}\left (x \right )^{3}+1207458 \mathrm {log}\left (x \right )^{2}-208487748 \,\mathrm {log}\left (x \right )+13499581683} \] Input:
int((2*exp(x)^2*log(x)^5+(30*exp(x)^3-2590*exp(x)^2)*log(x)^4+(180*exp(x)^ 4-31080*exp(x)^3+1341620*exp(x)^2+(-2-2*x)*exp(x))*log(x)^3+(540*exp(x)^5- 139860*exp(x)^4+12074580*exp(x)^3+(-6*x-347479598)*exp(x)^2+(1554*x+1558)* exp(x))*log(x)^2+(810*exp(x)^6-279720*exp(x)^5+36223740*exp(x)^4+(18*x-208 4877534)*exp(x)^3+(3108*x+44998614958)*exp(x)^2+(-402486*x-404558)*exp(x)+ 2*x)*log(x)+486*exp(x)^7-209790*exp(x)^6+36223740*exp(x)^5+(54*x-312731627 4)*exp(x)^4+(-4662*x+134995830852)*exp(x)^3+(-402486*x-2330928984272)*exp( x)^2+(-12*x^2+34747964*x+35016282)*exp(x)-522*x)/(log(x)^5+(15*exp(x)-1295 )*log(x)^4+(90*exp(x)^2-15540*exp(x)+670810)*log(x)^3+(270*exp(x)^3-69930* exp(x)^2+6037290*exp(x)-173739790)*log(x)^2+(405*exp(x)^4-139860*exp(x)^3+ 18111870*exp(x)^2-1042438740*exp(x)+22499302805)*log(x)+243*exp(x)^5-10489 5*exp(x)^4+18111870*exp(x)^3-1563658110*exp(x)^2+67497908415*exp(x)-116546 3885299),x)
Output:
(243*e**(6*x) + 324*e**(5*x)*log(x) - 83916*e**(5*x) + 162*e**(4*x)*log(x) **2 - 83916*e**(4*x)*log(x) + 5433561*e**(4*x) + 36*e**(3*x)*log(x)**3 - 2 7972*e**(3*x)*log(x)**2 - 54*e**(3*x)*x + 1250926488*e**(3*x) + 3*e**(2*x) *log(x)**4 - 3108*e**(2*x)*log(x)**3 - 2414916*e**(2*x)*log(x)**2 - 36*e** (2*x)*log(x)*x + 1667901984*e**(2*x)*log(x) + 9324*e**(2*x)*x - 2294928886 11*e**(2*x) - 804972*e**x*log(x)**3 - 6*e**x*log(x)**2*x + 625463244*e**x* log(x)**2 + 3108*e**x*log(x)*x - 161994980196*e**x*log(x) - 402486*e**x*x + 13985566623588*e**x - 67081*log(x)**4 + 69495916*log(x)**3 - 26999163366 *log(x)**2 + 4661855541196*log(x) + 3*x**2 - 301855146292441)/(3*(81*e**(4 *x) + 108*e**(3*x)*log(x) - 27972*e**(3*x) + 54*e**(2*x)*log(x)**2 - 27972 *e**(2*x)*log(x) + 3622374*e**(2*x) + 12*e**x*log(x)**3 - 9324*e**x*log(x) **2 + 2414916*e**x*log(x) - 208487748*e**x + log(x)**4 - 1036*log(x)**3 + 402486*log(x)**2 - 69495916*log(x) + 4499860561))