3.98.90 \(\int \frac {36223740 e^{5 x}-209790 e^{6 x}+486 e^{7 x}+e^{2 x} (-2330928984272-402486 x)+e^{3 x} (134995830852-4662 x)-522 x+e^{4 x} (-3127316274+54 x)+e^x (35016282+34747964 x-12 x^2)+(36223740 e^{4 x}-279720 e^{5 x}+810 e^{6 x}+e^x (-404558-402486 x)+2 x+e^{3 x} (-2084877534+18 x)+e^{2 x} (44998614958+3108 x)) \log (x)+(12074580 e^{3 x}-139860 e^{4 x}+540 e^{5 x}+e^{2 x} (-347479598-6 x)+e^x (1558+1554 x)) \log ^2(x)+(1341620 e^{2 x}-31080 e^{3 x}+180 e^{4 x}+e^x (-2-2 x)) \log ^3(x)+(-2590 e^{2 x}+30 e^{3 x}) \log ^4(x)+2 e^{2 x} \log ^5(x)}{-1165463885299+67497908415 e^x-1563658110 e^{2 x}[phone] e^{3 x}-104895 e^{4 x}+243 e^{5 x}+(22499302805-1042438740 e^x+18111870 e^{2 x}-139860 e^{3 x}+405 e^{4 x}) \log (x)+(-173739790+6037290 e^x-69930 e^{2 x}+270 e^{3 x}) \log ^2(x)+(670810-15540 e^x+90 e^{2 x}) \log ^3(x)+(-1295+15 e^x) \log ^4(x)+\log ^5(x)} \, dx\)

Optimal. Leaf size=22 \[ \left (e^x-\frac {x}{\left (259-3 e^x-\log (x)\right )^2}\right )^2 \]

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Rubi [F]  time = 5.21, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \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}[phone] 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 \end {gather*}

Verification is not applicable to the result.

[In]

Int[(36223740*E^(5*x) - 209790*E^(6*x) + 486*E^(7*x) + E^(2*x)*(-2330928984272 - 402486*x) + E^(3*x)*(13499583
0852 - 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)*(4
4998614958 + 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 - 1042438740*E^x + 18111870*E^(2*x) - 139
860*E^(3*x) + 405*E^(4*x))*Log[x] + (-173739790 + 6037290*E^x - 69930*E^(2*x) + 270*E^(3*x))*Log[x]^2 + (67081
0 - 15540*E^x + 90*E^(2*x))*Log[x]^3 + (-1295 + 15*E^x)*Log[x]^4 + Log[x]^5),x]

[Out]

E^(2*x) - 4*Defer[Int][x/(-259 + 3*E^x + Log[x])^5, x] - 1036*Defer[Int][x^2/(-259 + 3*E^x + Log[x])^5, x] + 4
*Defer[Int][(x^2*Log[x])/(-259 + 3*E^x + Log[x])^5, x] + 2*Defer[Int][x/(-259 + 3*E^x + Log[x])^4, x] - 4*Defe
r[Int][x^2/(-259 + 3*E^x + Log[x])^4, x] + (1036*Defer[Int][(-259 + 3*E^x + Log[x])^(-3), x])/3 + (268324*Defe
r[Int][x/(-259 + 3*E^x + Log[x])^3, x])/3 - (4*Defer[Int][Log[x]/(-259 + 3*E^x + Log[x])^3, x])/3 - (2072*Defe
r[Int][(x*Log[x])/(-259 + 3*E^x + Log[x])^3, x])/3 + (4*Defer[Int][(x*Log[x]^2)/(-259 + 3*E^x + Log[x])^3, x])
/3 - (514*Defer[Int][(-259 + 3*E^x + Log[x])^(-2), x])/3 + 518*Defer[Int][x/(-259 + 3*E^x + Log[x])^2, x] + (2
*Defer[Int][Log[x]/(-259 + 3*E^x + Log[x])^2, x])/3 - 2*Defer[Int][(x*Log[x])/(-259 + 3*E^x + Log[x])^2, x] -
(2*Defer[Int][(-259 + 3*E^x + Log[x])^(-1), x])/3 + (2*Defer[Int][x/(-259 + 3*E^x + Log[x]), x])/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (-18111870 e^{5 x}+104895 e^{6 x}-243 e^{7 x}-e^{3 x} (67497915426-2331 x)+261 x-9 e^{4 x} (-173739793+3 x)+259 e^{2 x} (4499862904+777 x)-e^x \left (17508141+17373982 x-6 x^2\right )-\left (18111870 e^{4 x}-139860 e^{5 x}+405 e^{6 x}+x+3 e^{3 x} (-347479589+3 x)-259 e^x (781+777 x)+e^{2 x} (22499307479+1554 x)\right ) \log (x)-e^x \left (779+6037290 e^{2 x}-69930 e^{3 x}+270 e^{4 x}+777 x-e^x (173739799+3 x)\right ) \log ^2(x)-e^x \left (-1+670810 e^x-15540 e^{2 x}+90 e^{3 x}-x\right ) \log ^3(x)-5 e^{2 x} \left (-259+3 e^x\right ) \log ^4(x)-e^{2 x} \log ^5(x)\right )}{\left (259-3 e^x-\log (x)\right )^5} \, dx\\ &=2 \int \frac {-18111870 e^{5 x}+104895 e^{6 x}-243 e^{7 x}-e^{3 x} (67497915426-2331 x)+261 x-9 e^{4 x} (-173739793+3 x)+259 e^{2 x} (4499862904+777 x)-e^x \left (17508141+17373982 x-6 x^2\right )-\left (18111870 e^{4 x}-139860 e^{5 x}+405 e^{6 x}+x+3 e^{3 x} (-347479589+3 x)-259 e^x (781+777 x)+e^{2 x} (22499307479+1554 x)\right ) \log (x)-e^x \left (779+6037290 e^{2 x}-69930 e^{3 x}+270 e^{4 x}+777 x-e^x (173739799+3 x)\right ) \log ^2(x)-e^x \left (-1+670810 e^x-15540 e^{2 x}+90 e^{3 x}-x\right ) \log ^3(x)-5 e^{2 x} \left (-259+3 e^x\right ) \log ^4(x)-e^{2 x} \log ^5(x)}{\left (259-3 e^x-\log (x)\right )^5} \, dx\\ &=2 \int \left (e^{2 x}-\frac {x (-1+2 x)}{\left (-259+3 e^x+\log (x)\right )^4}+\frac {-1+x}{3 \left (-259+3 e^x+\log (x)\right )}+\frac {2 x (-1-259 x+x \log (x))}{\left (-259+3 e^x+\log (x)\right )^5}+\frac {2 (-259+\log (x)) (-1-259 x+x \log (x))}{3 \left (-259+3 e^x+\log (x)\right )^3}-\frac {257-777 x-\log (x)+3 x \log (x)}{3 \left (-259+3 e^x+\log (x)\right )^2}\right ) \, dx\\ &=\frac {2}{3} \int \frac {-1+x}{-259+3 e^x+\log (x)} \, dx-\frac {2}{3} \int \frac {257-777 x-\log (x)+3 x \log (x)}{\left (-259+3 e^x+\log (x)\right )^2} \, dx+\frac {4}{3} \int \frac {(-259+\log (x)) (-1-259 x+x \log (x))}{\left (-259+3 e^x+\log (x)\right )^3} \, dx+2 \int e^{2 x} \, dx-2 \int \frac {x (-1+2 x)}{\left (-259+3 e^x+\log (x)\right )^4} \, dx+4 \int \frac {x (-1-259 x+x \log (x))}{\left (-259+3 e^x+\log (x)\right )^5} \, dx\\ &=e^{2 x}-\frac {2}{3} \int \left (\frac {257}{\left (-259+3 e^x+\log (x)\right )^2}-\frac {777 x}{\left (-259+3 e^x+\log (x)\right )^2}-\frac {\log (x)}{\left (-259+3 e^x+\log (x)\right )^2}+\frac {3 x \log (x)}{\left (-259+3 e^x+\log (x)\right )^2}\right ) \, dx+\frac {2}{3} \int \left (-\frac {1}{-259+3 e^x+\log (x)}+\frac {x}{-259+3 e^x+\log (x)}\right ) \, dx+\frac {4}{3} \int \left (\frac {259}{\left (-259+3 e^x+\log (x)\right )^3}+\frac {67081 x}{\left (-259+3 e^x+\log (x)\right )^3}-\frac {\log (x)}{\left (-259+3 e^x+\log (x)\right )^3}-\frac {518 x \log (x)}{\left (-259+3 e^x+\log (x)\right )^3}+\frac {x \log ^2(x)}{\left (-259+3 e^x+\log (x)\right )^3}\right ) \, dx-2 \int \left (-\frac {x}{\left (-259+3 e^x+\log (x)\right )^4}+\frac {2 x^2}{\left (-259+3 e^x+\log (x)\right )^4}\right ) \, dx+4 \int \left (-\frac {x}{\left (-259+3 e^x+\log (x)\right )^5}-\frac {259 x^2}{\left (-259+3 e^x+\log (x)\right )^5}+\frac {x^2 \log (x)}{\left (-259+3 e^x+\log (x)\right )^5}\right ) \, dx\\ &=e^{2 x}+\frac {2}{3} \int \frac {\log (x)}{\left (-259+3 e^x+\log (x)\right )^2} \, dx-\frac {2}{3} \int \frac {1}{-259+3 e^x+\log (x)} \, dx+\frac {2}{3} \int \frac {x}{-259+3 e^x+\log (x)} \, dx-\frac {4}{3} \int \frac {\log (x)}{\left (-259+3 e^x+\log (x)\right )^3} \, dx+\frac {4}{3} \int \frac {x \log ^2(x)}{\left (-259+3 e^x+\log (x)\right )^3} \, dx+2 \int \frac {x}{\left (-259+3 e^x+\log (x)\right )^4} \, dx-2 \int \frac {x \log (x)}{\left (-259+3 e^x+\log (x)\right )^2} \, dx-4 \int \frac {x}{\left (-259+3 e^x+\log (x)\right )^5} \, dx+4 \int \frac {x^2 \log (x)}{\left (-259+3 e^x+\log (x)\right )^5} \, dx-4 \int \frac {x^2}{\left (-259+3 e^x+\log (x)\right )^4} \, dx-\frac {514}{3} \int \frac {1}{\left (-259+3 e^x+\log (x)\right )^2} \, dx+\frac {1036}{3} \int \frac {1}{\left (-259+3 e^x+\log (x)\right )^3} \, dx+518 \int \frac {x}{\left (-259+3 e^x+\log (x)\right )^2} \, dx-\frac {2072}{3} \int \frac {x \log (x)}{\left (-259+3 e^x+\log (x)\right )^3} \, dx-1036 \int \frac {x^2}{\left (-259+3 e^x+\log (x)\right )^5} \, dx+\frac {268324}{3} \int \frac {x}{\left (-259+3 e^x+\log (x)\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.20, size = 38, normalized size = 1.73 \begin {gather*} 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} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(36223740*E^(5*x) - 209790*E^(6*x) + 486*E^(7*x) + E^(2*x)*(-2330928984272 - 402486*x) + E^(3*x)*(13
4995830852 - 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] + (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 - 156365811
0*E^(2*x) + 18111870*E^(3*x) - 104895*E^(4*x) + 243*E^(5*x) + (22499302805 - 1042438740*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]

[Out]

E^(2*x) + x^2/(-259 + 3*E^x + Log[x])^4 - (2*E^x*x)/(-259 + 3*E^x + Log[x])^2

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fricas [B]  time = 0.84, size = 227, normalized size = 10.32 \begin {gather*} \frac {e^{\left (2 \, x\right )} \log \relax (x)^{4} + 4 \, {\left (3 \, e^{\left (3 \, x\right )} - 259 \, e^{\left (2 \, x\right )}\right )} \log \relax (x)^{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 \relax (x)^{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 \relax (x) + 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 \relax (x)^{3} + \log \relax (x)^{4} + 6 \, {\left (9 \, e^{\left (2 \, x\right )} - 1554 \, e^{x} + 67081\right )} \log \relax (x)^{2} + 4 \, {\left (27 \, e^{\left (3 \, x\right )} - 6993 \, e^{\left (2 \, x\right )} + 603729 \, e^{x} - 17373979\right )} \log \relax (x) + 81 \, e^{\left (4 \, x\right )} - 27972 \, e^{\left (3 \, x\right )} + 3622374 \, e^{\left (2 \, x\right )} - 208487748 \, e^{x} + 4499860561} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((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*x-2)*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+44
998614958)*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
-3127316274)*exp(x)^4+(-4662*x+134995830852)*exp(x)^3+(-402486*x-2330928984272)*exp(x)^2+(-12*x^2+34747964*x+3
5016282)*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)^2-104243
8740*exp(x)[phone])*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")

[Out]

(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 + 173
73979)*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)

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giac [B]  time = 1.39, size = 264, normalized size = 12.00 \begin {gather*} \frac {e^{\left (2 \, x\right )} \log \relax (x)^{4} - 2 \, x e^{x} \log \relax (x)^{2} + 12 \, e^{\left (3 \, x\right )} \log \relax (x)^{3} - 1036 \, e^{\left (2 \, x\right )} \log \relax (x)^{3} - 12 \, x e^{\left (2 \, x\right )} \log \relax (x) + 1036 \, x e^{x} \log \relax (x) + 54 \, e^{\left (4 \, x\right )} \log \relax (x)^{2} - 9324 \, e^{\left (3 \, x\right )} \log \relax (x)^{2} + 402486 \, e^{\left (2 \, x\right )} \log \relax (x)^{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 \relax (x) - 27972 \, e^{\left (4 \, x\right )} \log \relax (x) + 2414916 \, e^{\left (3 \, x\right )} \log \relax (x) - 69495916 \, e^{\left (2 \, x\right )} \log \relax (x) + 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 \relax (x)^{3} + \log \relax (x)^{4} + 54 \, e^{\left (2 \, x\right )} \log \relax (x)^{2} - 9324 \, e^{x} \log \relax (x)^{2} - 1036 \, \log \relax (x)^{3} + 108 \, e^{\left (3 \, x\right )} \log \relax (x) - 27972 \, e^{\left (2 \, x\right )} \log \relax (x) + 2414916 \, e^{x} \log \relax (x) + 402486 \, \log \relax (x)^{2} + 81 \, e^{\left (4 \, x\right )} - 27972 \, e^{\left (3 \, x\right )} + 3622374 \, e^{\left (2 \, x\right )} - 208487748 \, e^{x} - 69495916 \, \log \relax (x) + 4499860561} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((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*x-2)*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+44
998614958)*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
-3127316274)*exp(x)^4+(-4662*x+134995830852)*exp(x)^3+(-402486*x-2330928984272)*exp(x)^2+(-12*x^2+34747964*x+3
5016282)*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)^2-104243
8740*exp(x)[phone])*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")

[Out]

(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) + 103
6*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) +
3108*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*log(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) + 402486*log(x)^2 + 81*e^(4*x) - 27972*e^(3*x) + 3622374*e^(2*x) - 20848774
8*e^x - 69495916*log(x) + 4499860561)

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maple [B]  time = 0.08, size = 58, normalized size = 2.64

method	result	size
risch	\({\mathrm e}^{2 x}+\frac {x \left (-18 \,{\mathrm e}^{3 x}-12 \ln \relax (x ) {\mathrm e}^{2 x}-2 \,{\mathrm e}^{x} \ln \relax (x )^{2}+3108 \,{\mathrm e}^{2 x}+1036 \,{\mathrm e}^{x} \ln \relax (x )+x -134162 \,{\mathrm e}^{x}\right )}{\left (\ln \relax (x )+3 \,{\mathrm e}^{x}-259\right )^{4}}\)	\(58\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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*
x-2)*exp(x))*ln(x)^3+(540*exp(x)^5-139860*exp(x)^4+12074580*exp(x)^3+(-6*x-347479598)*exp(x)^2+(1554*x+1558)*e
xp(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+(-402486*x-404558)*exp(x)+2*x)*ln(x)+486*exp(x)^7-209790*exp(x)^6+36223740*exp(x)^5+(54*x-3127316274
)*exp(x)^4+(-4662*x+134995830852)*exp(x)^3+(-402486*x-2330928984272)*exp(x)^2+(-12*x^2+34747964*x+35016282)*ex
p(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*ex
p(x)^2+6037290*exp(x)-173739790)*ln(x)^2+(405*exp(x)^4-139860*exp(x)^3+18111870*exp(x)^2-1042438740*exp(x)+224
99302805)*ln(x)+243*exp(x)^5-104895*exp(x)^4+18111870*exp(x)^3-1563658110*exp(x)^2+67497908415*exp(x)-11654638
85299),x,method=_RETURNVERBOSE)

[Out]

exp(2*x)+x*(-18*exp(3*x)-12*ln(x)*exp(2*x)-2*exp(x)*ln(x)^2+3108*exp(2*x)+1036*exp(x)*ln(x)+x-134162*exp(x))/(
ln(x)+3*exp(x)-259)^4

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maxima [B]  time = 0.80, size = 194, normalized size = 8.82 \begin {gather*} \frac {x^{2} + 108 \, {\left (\log \relax (x) - 259\right )} e^{\left (5 \, x\right )} + 54 \, {\left (\log \relax (x)^{2} - 518 \, \log \relax (x) + 67081\right )} e^{\left (4 \, x\right )} + 6 \, {\left (2 \, \log \relax (x)^{3} - 1554 \, \log \relax (x)^{2} - 3 \, x + 402486 \, \log \relax (x) - 34747958\right )} e^{\left (3 \, x\right )} + {\left (\log \relax (x)^{4} - 1036 \, \log \relax (x)^{3} - 4 \, {\left (3 \, x + 17373979\right )} \log \relax (x) + 402486 \, \log \relax (x)^{2} + 3108 \, x + 4499860561\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x \log \relax (x)^{2} - 518 \, x \log \relax (x) + 67081 \, x\right )} e^{x} + 81 \, e^{\left (6 \, x\right )}}{\log \relax (x)^{4} - 1036 \, \log \relax (x)^{3} + 108 \, {\left (\log \relax (x) - 259\right )} e^{\left (3 \, x\right )} + 54 \, {\left (\log \relax (x)^{2} - 518 \, \log \relax (x) + 67081\right )} e^{\left (2 \, x\right )} + 12 \, {\left (\log \relax (x)^{3} - 777 \, \log \relax (x)^{2} + 201243 \, \log \relax (x) - 17373979\right )} e^{x} + 402486 \, \log \relax (x)^{2} + 81 \, e^{\left (4 \, x\right )} - 69495916 \, \log \relax (x) + 4499860561} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((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*x-2)*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+44
998614958)*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
-3127316274)*exp(x)^4+(-4662*x+134995830852)*exp(x)^3+(-402486*x-2330928984272)*exp(x)^2+(-12*x^2+34747964*x+3
5016282)*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)^2-104243
8740*exp(x)[phone])*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")

[Out]

(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*lo
g(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*l
og(x)^2 + 201243*log(x) - 17373979)*e^x + 402486*log(x)^2 + 81*e^(4*x) - 69495916*log(x) + 4499860561)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {2\,{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^5+\left (30\,{\mathrm {e}}^{3\,x}-2590\,{\mathrm {e}}^{2\,x}\right )\,{\ln \relax (x)}^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 \relax (x)}^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 \relax (x)}^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 \relax (x)-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 \relax (x)}^5+\left (15\,{\mathrm {e}}^x-1295\right )\,{\ln \relax (x)}^4+\left (90\,{\mathrm {e}}^{2\,x}-15540\,{\mathrm {e}}^x+670810\right )\,{\ln \relax (x)}^3+\left (270\,{\mathrm {e}}^{3\,x}-69930\,{\mathrm {e}}^{2\,x}+6037290\,{\mathrm {e}}^x-173739790\right )\,{\ln \relax (x)}^2+\left (18111870\,{\mathrm {e}}^{2\,x}-139860\,{\mathrm {e}}^{3\,x}+405\,{\mathrm {e}}^{4\,x}-1042438740\,{\mathrm {e}}^x+22499302805\right )\,\ln \relax (x)-1563658110\,{\mathrm {e}}^{2\,x}[phone]\,{\mathrm {e}}^{3\,x}-104895\,{\mathrm {e}}^{4\,x}+243\,{\mathrm {e}}^{5\,x}[phone]\,{\mathrm {e}}^x-1165463885299} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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 + 1558) - 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*exp(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)
+ exp(3*x)*(18*x - 2084877534) - exp(x)*(402486*x + 404558)) - exp(2*x)*(402486*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) - 1563
658110*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) + 22499302805) + log(x)^4*(15*exp(x) - 1295) + log(x)^5 - log(x)^2*(6
9930*exp(2*x) - 270*exp(3*x) - 6037290*exp(x) + 173739790) + log(x)^3*(90*exp(2*x) - 15540*exp(x) + 670810) -
1165463885299),x)

[Out]

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 + 1558) - 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*exp(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)
+ exp(3*x)*(18*x - 2084877534) - exp(x)*(402486*x + 404558)) - exp(2*x)*(402486*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) - 1563
658110*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) + 22499302805) + log(x)^4*(15*exp(x) - 1295) + log(x)^5 - log(x)^2*(6
9930*exp(2*x) - 270*exp(3*x) - 6037290*exp(x) + 173739790) + log(x)^3*(90*exp(2*x) - 15540*exp(x) + 670810) -
1165463885299), x)

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sympy [B]  time = 0.81, size = 139, normalized size = 6.32 \begin {gather*} \frac {x^{2} - 18 x e^{3 x} + \left (- 12 x \log {\relax (x )} + 3108 x\right ) e^{2 x} + \left (- 2 x \log {\relax (x )}^{2} + 1036 x \log {\relax (x )} - 134162 x\right ) e^{x}}{\left (108 \log {\relax (x )} - 27972\right ) e^{3 x} + \left (54 \log {\relax (x )}^{2} - 27972 \log {\relax (x )} + 3622374\right ) e^{2 x} + \left (12 \log {\relax (x )}^{3} - 9324 \log {\relax (x )}^{2} + 2414916 \log {\relax (x )} - 208487748\right ) e^{x} + 81 e^{4 x} + \log {\relax (x )}^{4} - 1036 \log {\relax (x )}^{3} + 402486 \log {\relax (x )}^{2} - 69495916 \log {\relax (x )} + 4499860561} + e^{2 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((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*x-2)*exp(x))*ln(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))*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+(-402486*x-404558)*exp(x)+2*x)*ln(x)+486*exp(x)**7-209790*exp(x)**6+3622374
0*exp(x)**5+(54*x-3127316274)*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)/(ln(x)**5+(15*exp(x)-1295)*ln(x)**4+(90*exp(x)**2-15540*exp(x)+670
810)*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)[phone])*ln(x)+243*exp(x)**5-104895*exp(x)**4+18111870*exp(x)**3-15
63658110*exp(x)**2+67497908415*exp(x)-1165463885299),x)

[Out]

(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 - 694
95916*log(x) + 4499860561) + exp(2*x)

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