3.86.60 \(\int \frac {2916 x-2916 x^2+e^3 (-972 x^2+972 x^3)+e^6 (108 x^3-108 x^4)+e^9 (-4 x^4+4 x^5)+(x^2)^{10+2 x} (58320+8748 x+e^3 (-19440 x-2916 x^2)+e^6 (2160 x^2+324 x^3)+e^9 (-80 x^3-12 x^4)+(5832 x-1944 e^3 x^2+216 e^6 x^3-8 e^9 x^4) \log (x^2))+(e^3 (972 x-972 x^2)+e^6 (-216 x^2+216 x^3)+e^9 (12 x^3-12 x^4)+(x^2)^{10+2 x} (e^3 (19440+2916 x)+e^6 (-4320 x-648 x^2)+e^9 (240 x^2+36 x^3)+(1944 e^3 x-432 e^6 x^2+24 e^9 x^3) \log (x^2))) \log (x+(x^2)^{10+2 x})+(e^6 (108 x-108 x^2)+e^9 (-12 x^2+12 x^3)+(x^2)^{10+2 x} (e^6 (2160+324 x)+e^9 (-240 x-36 x^2)+(216 e^6 x-24 e^9 x^2) \log (x^2))) \log ^2(x+(x^2)^{10+2 x})+(e^9 (4 x-4 x^2)+(x^2)^{10+2 x} (e^9 (80+12 x)+8 e^9 x \log (x^2))) \log ^3(x+(x^2)^{10+2 x})}{e^9 x^2+e^9 x (x^2)^{10+2 x}} \, dx\)
Optimal. Leaf size=23 \[ \left (-\frac {9}{e^3}+x-\log \left (x+\left (x^2\right )^{2 (5+x)}\right )\right )^4 \]
________________________________________________________________________________________
Rubi [F] time = 35.04, 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 {2916 x-2916 x^2+e^3 \left (-972 x^2+972 x^3\right )+e^6 \left (108 x^3-108 x^4\right )+e^9 \left (-4 x^4+4 x^5\right )+\left (x^2\right )^{10+2 x} \left (58320+8748 x+e^3 \left (-19440 x-2916 x^2\right )+e^6 \left (2160 x^2+324 x^3\right )+e^9 \left (-80 x^3-12 x^4\right )+\left (5832 x-1944 e^3 x^2+216 e^6 x^3-8 e^9 x^4\right ) \log \left (x^2\right )\right )+\left (e^3 \left (972 x-972 x^2\right )+e^6 \left (-216 x^2+216 x^3\right )+e^9 \left (12 x^3-12 x^4\right )+\left (x^2\right )^{10+2 x} \left (e^3 (19440+2916 x)+e^6 \left (-4320 x-648 x^2\right )+e^9 \left (240 x^2+36 x^3\right )+\left (1944 e^3 x-432 e^6 x^2+24 e^9 x^3\right ) \log \left (x^2\right )\right )\right ) \log \left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^6 \left (108 x-108 x^2\right )+e^9 \left (-12 x^2+12 x^3\right )+\left (x^2\right )^{10+2 x} \left (e^6 (2160+324 x)+e^9 \left (-240 x-36 x^2\right )+\left (216 e^6 x-24 e^9 x^2\right ) \log \left (x^2\right )\right )\right ) \log ^2\left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^9 \left (4 x-4 x^2\right )+\left (x^2\right )^{10+2 x} \left (e^9 (80+12 x)+8 e^9 x \log \left (x^2\right )\right )\right ) \log ^3\left (x+\left (x^2\right )^{10+2 x}\right )}{e^9 x^2+e^9 x \left (x^2\right )^{10+2 x}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(2916*x - 2916*x^2 + E^3*(-972*x^2 + 972*x^3) + E^6*(108*x^3 - 108*x^4) + E^9*(-4*x^4 + 4*x^5) + (x^2)^(10
+ 2*x)*(58320 + 8748*x + E^3*(-19440*x - 2916*x^2) + E^6*(2160*x^2 + 324*x^3) + E^9*(-80*x^3 - 12*x^4) + (583
2*x - 1944*E^3*x^2 + 216*E^6*x^3 - 8*E^9*x^4)*Log[x^2]) + (E^3*(972*x - 972*x^2) + E^6*(-216*x^2 + 216*x^3) +
E^9*(12*x^3 - 12*x^4) + (x^2)^(10 + 2*x)*(E^3*(19440 + 2916*x) + E^6*(-4320*x - 648*x^2) + E^9*(240*x^2 + 36*x
^3) + (1944*E^3*x - 432*E^6*x^2 + 24*E^9*x^3)*Log[x^2]))*Log[x + (x^2)^(10 + 2*x)] + (E^6*(108*x - 108*x^2) +
E^9*(-12*x^2 + 12*x^3) + (x^2)^(10 + 2*x)*(E^6*(2160 + 324*x) + E^9*(-240*x - 36*x^2) + (216*E^6*x - 24*E^9*x^
2)*Log[x^2]))*Log[x + (x^2)^(10 + 2*x)]^2 + (E^9*(4*x - 4*x^2) + (x^2)^(10 + 2*x)*(E^9*(80 + 12*x) + 8*E^9*x*L
og[x^2]))*Log[x + (x^2)^(10 + 2*x)]^3)/(E^9*x^2 + E^9*x*(x^2)^(10 + 2*x)),x]
[Out]
(-11664*x)/E^9 + (77760*x)/E^6 + (86400*x)/E^3 - 1200*x^2 + (1944*x^2)/E^6 + (4320*x^2)/E^3 - (1280*x^3)/9 - (
16*x^3)/E^3 - 2*x^4 - (3*(9 - E^3*x)^4)/E^12 + (26244*Log[x])/E^12 + (58320*Log[x])/E^9 + (4860*x^2*Log[x^2])/
E^6 + (4320*x^2*Log[x^2])/E^3 - 80*x^3*Log[x^2] - (120*x^3*Log[x^2])/E^3 + (2*x^4*Log[x^2])/3 - (2*(9 - E^3*x)
^4*Log[x^2])/E^12 - (3888*(10*x + x^2)*Log[x^2])/E^6 + (144*(15*x^2 + 2*x^3)*Log[x^2])/E^3 - (8*(20*x^3 + 3*x^
4)*Log[x^2])/3 - (1944*x^2*Log[x^2]^2)/E^6 + (144*x^3*Log[x^2]^2)/E^3 - 4*x^4*Log[x^2]^2 - (972*x*Log[x + (x^2
)^(2*(5 + x))])/E^6 - (4320*x*Log[x + (x^2)^(2*(5 + x))])/E^3 + 120*x^2*Log[x + (x^2)^(2*(5 + x))] - (108*x^2*
Log[x + (x^2)^(2*(5 + x))])/E^3 + (20*x^3*Log[x + (x^2)^(2*(5 + x))])/3 + (1944*x*Log[x^2]*Log[x + (x^2)^(2*(5
+ x))])/E^6 - (216*x^2*Log[x^2]*Log[x + (x^2)^(2*(5 + x))])/E^3 + 8*x^3*Log[x^2]*Log[x + (x^2)^(2*(5 + x))] -
(18468*Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x])/E^6 - (82080*Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x])/E
^3 - (972*(12 - 19*E^3)*Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x])/E^9 - (5832*Log[x^2]*Defer[Int][(1 + x^19*
(x^2)^(2*x))^(-1), x])/E^9 + (36936*Log[x^2]*Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x])/E^6 - (216*(18 - 19*E
^3)*Log[x + (x^2)^(2*(5 + x))]*Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x])/E^6 - (1944*Log[x^2]*Log[x + (x^2)^
(2*(5 + x))]*Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x])/E^6 - (55404*Defer[Int][1/(x*(1 + x^19*(x^2)^(2*x))),
x])/E^9 - (18468*Log[x + (x^2)^(2*(5 + x))]*Defer[Int][1/(x*(1 + x^19*(x^2)^(2*x))), x])/E^6 + 2280*Defer[Int
][x/(1 + x^19*(x^2)^(2*x)), x] - (3888*Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x])/E^6 - (19332*Defer[Int][x/(1 +
x^19*(x^2)^(2*x)), x])/E^3 + (108*(36 - 19*E^3)*Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x])/E^6 + (7776*Log[x^2]
*Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x])/E^6 - (12744*Log[x^2]*Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x])/E^3 +
(12*(72 - 19*E^3)*Log[x + (x^2)^(2*(5 + x))]*Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x])/E^3 + (432*Log[x^2]*Log
[x + (x^2)^(2*(5 + x))]*Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x])/E^3 + (1820*Defer[Int][x^2/(1 + x^19*(x^2)^(2
*x)), x])/3 - (432*Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x])/E^3 - (4*(108 - 19*E^3)*Defer[Int][x^2/(1 + x^19
*(x^2)^(2*x)), x])/E^3 + 392*Log[x^2]*Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x] - (1296*Log[x^2]*Defer[Int][x^
2/(1 + x^19*(x^2)^(2*x)), x])/E^3 - 48*Log[x + (x^2)^(2*(5 + x))]*Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x] -
24*Log[x^2]*Log[x + (x^2)^(2*(5 + x))]*Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x] + (128*Defer[Int][x^3/(1 + x^
19*(x^2)^(2*x)), x])/3 + (160*Log[x^2]*Defer[Int][x^3/(1 + x^19*(x^2)^(2*x)), x])/3 + (3888*Defer[Int][(x*Log[
x^2]^2)/(1 + x^19*(x^2)^(2*x)), x])/E^6 - (432*Defer[Int][(x^2*Log[x^2]^2)/(1 + x^19*(x^2)^(2*x)), x])/E^3 + 1
6*Defer[Int][(x^3*Log[x^2]^2)/(1 + x^19*(x^2)^(2*x)), x] + (19440*Defer[Int][Log[x + (x^2)^(2*(5 + x))]/x, x])
/E^6 - 240*Defer[Int][Log[x + (x^2)^(2*(5 + x))]^2, x] + (324*Defer[Int][Log[x + (x^2)^(2*(5 + x))]^2, x])/E^3
+ (2160*Defer[Int][Log[x + (x^2)^(2*(5 + x))]^2/x, x])/E^3 - 36*Defer[Int][x*Log[x + (x^2)^(2*(5 + x))]^2, x]
- (12*(36 - 19*E^3)*Defer[Int][Log[x + (x^2)^(2*(5 + x))]^2/(1 + x^19*(x^2)^(2*x)), x])/E^3 - (2052*Defer[Int
][Log[x + (x^2)^(2*(5 + x))]^2/(x*(1 + x^19*(x^2)^(2*x))), x])/E^3 + 48*Defer[Int][(x*Log[x + (x^2)^(2*(5 + x)
)]^2)/(1 + x^19*(x^2)^(2*x)), x] + (216*Defer[Int][Log[x^2]*Log[x + (x^2)^(2*(5 + x))]^2, x])/E^3 - 24*Defer[I
nt][x*Log[x^2]*Log[x + (x^2)^(2*(5 + x))]^2, x] - (216*Defer[Int][(Log[x^2]*Log[x + (x^2)^(2*(5 + x))]^2)/(1 +
x^19*(x^2)^(2*x)), x])/E^3 + 24*Defer[Int][(x*Log[x^2]*Log[x + (x^2)^(2*(5 + x))]^2)/(1 + x^19*(x^2)^(2*x)),
x] + 12*Defer[Int][Log[x + (x^2)^(2*(5 + x))]^3, x] + 80*Defer[Int][Log[x + (x^2)^(2*(5 + x))]^3/x, x] - 16*De
fer[Int][Log[x + (x^2)^(2*(5 + x))]^3/(1 + x^19*(x^2)^(2*x)), x] - 76*Defer[Int][Log[x + (x^2)^(2*(5 + x))]^3/
(x*(1 + x^19*(x^2)^(2*x))), x] + 8*Defer[Int][Log[x^2]*Log[x + (x^2)^(2*(5 + x))]^3, x] - 8*Defer[Int][(Log[x^
2]*Log[x + (x^2)^(2*(5 + x))]^3)/(1 + x^19*(x^2)^(2*x)), x] + (864*(18 - 19*E^3)*Defer[Int][Defer[Int][(1 + x^
19*(x^2)^(2*x))^(-1), x], x])/E^6 + (7776*Log[x^2]*Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x], x])/
E^6 + (432*(18 - 19*E^3)*Log[x^2]*Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x], x])/E^6 + (11664*Defe
r[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/x, x])/E^9 - (73872*Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2
*x))^(-1), x]/x, x])/E^6 + (4320*(18 - 19*E^3)*Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/x, x])/E^
6 + (38880*Log[x^2]*Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/x, x])/E^6 + (3888*Log[x + (x^2)^(2*
(5 + x))]*Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/x, x])/E^6 - (864*(18 - 19*E^3)*Defer[Int][Def
er[Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/(1 + x^19*(x^2)^(2*x)), x])/E^6 - (7776*Log[x^2]*Defer[Int][Defer[Int]
[(1 + x^19*(x^2)^(2*x))^(-1), x]/(1 + x^19*(x^2)^(2*x)), x])/E^6 - (432*(18 - 19*E^3)*Log[x^2]*Defer[Int][Defe
r[Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/(1 + x^19*(x^2)^(2*x)), x])/E^6 - (4104*(18 - 19*E^3)*Defer[Int][Defer[
Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/(x*(1 + x^19*(x^2)^(2*x))), x])/E^6 - (36936*Log[x^2]*Defer[Int][Defer[In
t][(1 + x^19*(x^2)^(2*x))^(-1), x]/(x*(1 + x^19*(x^2)^(2*x))), x])/E^6 + (3888*Defer[Int][Log[x^2]^2*Defer[Int
][(1 + x^19*(x^2)^(2*x))^(-1), x], x])/E^6 - (3888*Defer[Int][(Log[x^2]^2*Defer[Int][(1 + x^19*(x^2)^(2*x))^(-
1), x])/(1 + x^19*(x^2)^(2*x)), x])/E^6 - (48*(72 - 19*E^3)*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]
, x])/E^3 - (1728*Log[x^2]*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x], x])/E^3 - (24*(72 - 19*E^3)*Log
[x^2]*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x], x])/E^3 - (15552*Defer[Int][Defer[Int][x/(1 + x^19*(
x^2)^(2*x)), x]/x, x])/E^6 + (25488*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^3 - (240*(72 -
19*E^3)*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^3 - (8640*Log[x^2]*Defer[Int][Defer[Int][
x/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^3 - (864*Log[x + (x^2)^(2*(5 + x))]*Defer[Int][Defer[Int][x/(1 + x^19*(x
^2)^(2*x)), x]/x, x])/E^3 + (48*(72 - 19*E^3)*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/(1 + x^19*(x^
2)^(2*x)), x])/E^3 + (1728*Log[x^2]*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/(1 + x^19*(x^2)^(2*x)),
x])/E^3 + (24*(72 - 19*E^3)*Log[x^2]*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/(1 + x^19*(x^2)^(2*x)
), x])/E^3 + (228*(72 - 19*E^3)*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/(x*(1 + x^19*(x^2)^(2*x))),
x])/E^3 + (8208*Log[x^2]*Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/(x*(1 + x^19*(x^2)^(2*x))), x])/E
^3 - (864*Defer[Int][Log[x^2]^2*Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x], x])/E^3 + (864*Defer[Int][(Log[x^2]^2
*Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x])/(1 + x^19*(x^2)^(2*x)), x])/E^3 + 192*Defer[Int][Defer[Int][x^2/(1 +
x^19*(x^2)^(2*x)), x], x] + 192*Log[x^2]*Defer[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x], x] + 176*Defer
[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/x, x] + (2592*Defer[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x))
, x]/x, x])/E^3 + 480*Log[x^2]*Defer[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/x, x] + 48*Log[x + (x^2)^(
2*(5 + x))]*Defer[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/x, x] - 192*Defer[Int][Defer[Int][x^2/(1 + x^
19*(x^2)^(2*x)), x]/(1 + x^19*(x^2)^(2*x)), x] - 192*Log[x^2]*Defer[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x))
, x]/(1 + x^19*(x^2)^(2*x)), x] - 912*Defer[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/(x*(1 + x^19*(x^2)^
(2*x))), x] - 456*Log[x^2]*Defer[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/(x*(1 + x^19*(x^2)^(2*x))), x]
+ 48*Defer[Int][Log[x^2]^2*Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x], x] - 48*Defer[Int][(Log[x^2]^2*Defer[In
t][x^2/(1 + x^19*(x^2)^(2*x)), x])/(1 + x^19*(x^2)^(2*x)), x] - (320*Defer[Int][Defer[Int][x^3/(1 + x^19*(x^2)
^(2*x)), x]/x, x])/3 + (73872*Defer[Int][Defer[Int][(x + x^20*(x^2)^(2*x))^(-1), x], x])/E^6 + (36936*Log[x^2]
*Defer[Int][Defer[Int][(x + x^20*(x^2)^(2*x))^(-1), x], x])/E^6 + (369360*Defer[Int][Defer[Int][(x + x^20*(x^2
)^(2*x))^(-1), x]/x, x])/E^6 - (73872*Defer[Int][Defer[Int][(x + x^20*(x^2)^(2*x))^(-1), x]/(1 + x^19*(x^2)^(2
*x)), x])/E^6 - (36936*Log[x^2]*Defer[Int][Defer[Int][(x + x^20*(x^2)^(2*x))^(-1), x]/(1 + x^19*(x^2)^(2*x)),
x])/E^6 - (350892*Defer[Int][Defer[Int][(x + x^20*(x^2)^(2*x))^(-1), x]/(x*(1 + x^19*(x^2)^(2*x))), x])/E^6 -
(15552*Defer[Int][Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x], x]/x, x])/E^6 - (864*(18 - 19*E^3)*De
fer[Int][Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x], x]/x, x])/E^6 - (15552*Defer[Int][Defer[Int][D
efer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/x, x], x])/E^6 - (7776*Log[x^2]*Defer[Int][Defer[Int][Defer[Int][(1
+ x^19*(x^2)^(2*x))^(-1), x]/x, x], x])/E^6 - (155520*Defer[Int][Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^
(-1), x]/x, x]/x, x])/E^6 + (15552*Defer[Int][Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/x, x]/(1 +
x^19*(x^2)^(2*x)), x])/E^6 + (7776*Log[x^2]*Defer[Int][Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x]/
x, x]/(1 + x^19*(x^2)^(2*x)), x])/E^6 + (73872*Defer[Int][Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(-1), x
]/x, x]/(x*(1 + x^19*(x^2)^(2*x))), x])/E^6 + (15552*Defer[Int][Defer[Int][Defer[Int][(1 + x^19*(x^2)^(2*x))^(
-1), x]/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^6 + (864*(18 - 19*E^3)*Defer[Int][Defer[Int][Defer[Int][(1 + x^19*
(x^2)^(2*x))^(-1), x]/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^6 + (73872*Defer[Int][Defer[Int][Defer[Int][(1 + x^1
9*(x^2)^(2*x))^(-1), x]/(x + x^20*(x^2)^(2*x)), x]/x, x])/E^6 + (3456*Defer[Int][Defer[Int][Defer[Int][x/(1 +
x^19*(x^2)^(2*x)), x], x]/x, x])/E^3 + (48*(72 - 19*E^3)*Defer[Int][Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2
*x)), x], x]/x, x])/E^3 + (3456*Defer[Int][Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/x, x], x])/E^3 +
(1728*Log[x^2]*Defer[Int][Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/x, x], x])/E^3 + (34560*Defer[In
t][Defer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/x, x]/x, x])/E^3 - (3456*Defer[Int][Defer[Int][Defer[Int
][x/(1 + x^19*(x^2)^(2*x)), x]/x, x]/(1 + x^19*(x^2)^(2*x)), x])/E^3 - (1728*Log[x^2]*Defer[Int][Defer[Int][De
fer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/x, x]/(1 + x^19*(x^2)^(2*x)), x])/E^3 - (16416*Defer[Int][Defer[Int][Def
er[Int][x/(1 + x^19*(x^2)^(2*x)), x]/x, x]/(x*(1 + x^19*(x^2)^(2*x))), x])/E^3 - (3456*Defer[Int][Defer[Int][D
efer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^3 - (48*(72 - 19*E^3)*Defer[Int][De
fer[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^3 - (16416*Defer[Int][Def
er[Int][Defer[Int][x/(1 + x^19*(x^2)^(2*x)), x]/(x + x^20*(x^2)^(2*x)), x]/x, x])/E^3 - 384*Defer[Int][Defer[I
nt][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x], x]/x, x] - 192*Defer[Int][Defer[Int][Defer[Int][x^2/(1 + x^19*(
x^2)^(2*x)), x]/x, x], x] - 96*Log[x^2]*Defer[Int][Defer[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/x, x],
x] - 1920*Defer[Int][Defer[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/x, x]/x, x] + 192*Defer[Int][Defer[
Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/x, x]/(1 + x^19*(x^2)^(2*x)), x] + 96*Log[x^2]*Defer[Int][Defer
[Int][Defer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/x, x]/(1 + x^19*(x^2)^(2*x)), x] + 912*Defer[Int][Defer[Int][D
efer[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/x, x]/(x*(1 + x^19*(x^2)^(2*x))), x] + 384*Defer[Int][Defer[Int][Defe
r[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/(1 + x^19*(x^2)^(2*x)), x]/x, x] + 912*Defer[Int][Defer[Int][Defer[Int][
x^2/(1 + x^19*(x^2)^(2*x)), x]/(x + x^20*(x^2)^(2*x)), x]/x, x] - (73872*Defer[Int][Defer[Int][Defer[Int][(x +
x^20*(x^2)^(2*x))^(-1), x], x]/x, x])/E^6 + (73872*Defer[Int][Defer[Int][Defer[Int][(x + x^20*(x^2)^(2*x))^(-
1), x]/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^6 + (15552*Defer[Int][Defer[Int][Defer[Int][Defer[Int][(1 + x^19*(x
^2)^(2*x))^(-1), x]/x, x], x]/x, x])/E^6 - (15552*Defer[Int][Defer[Int][Defer[Int][Defer[Int][(1 + x^19*(x^2)^
(2*x))^(-1), x]/x, x]/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^6 - (3456*Defer[Int][Defer[Int][Defer[Int][Defer[Int
][x/(1 + x^19*(x^2)^(2*x)), x]/x, x], x]/x, x])/E^3 + (3456*Defer[Int][Defer[Int][Defer[Int][Defer[Int][x/(1 +
x^19*(x^2)^(2*x)), x]/x, x]/(1 + x^19*(x^2)^(2*x)), x]/x, x])/E^3 + 192*Defer[Int][Defer[Int][Defer[Int][Defe
r[Int][x^2/(1 + x^19*(x^2)^(2*x)), x]/x, x], x]/x, x] - 192*Defer[Int][Defer[Int][Defer[Int][Defer[Int][x^2/(1
+ x^19*(x^2)^(2*x)), x]/x, x]/(1 + x^19*(x^2)^(2*x)), x]/x, x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (1-x+20 x^{19} \left (x^2\right )^{2 x}+3 x^{20} \left (x^2\right )^{2 x}+2 x^{20} \left (x^2\right )^{2 x} \log \left (x^2\right )\right ) \left (9-e^3 x+e^3 \log \left (x+\left (x^2\right )^{2 (5+x)}\right )\right )^3}{e^9 \left (x+x^{20} \left (x^2\right )^{2 x}\right )} \, dx\\ &=\frac {4 \int \frac {\left (1-x+20 x^{19} \left (x^2\right )^{2 x}+3 x^{20} \left (x^2\right )^{2 x}+2 x^{20} \left (x^2\right )^{2 x} \log \left (x^2\right )\right ) \left (9-e^3 x+e^3 \log \left (x+\left (x^2\right )^{2 (5+x)}\right )\right )^3}{x+x^{20} \left (x^2\right )^{2 x}} \, dx}{e^9}\\ &=\frac {4 \int \left (-\frac {\left (20+3 x+2 x \log \left (x^2\right )\right ) \left (-9+e^3 x-e^3 \log \left (x+\left (x^2\right )^{2 (5+x)}\right )\right )^3}{x}+\frac {\left (19+4 x+2 x \log \left (x^2\right )\right ) \left (-9+e^3 x-e^3 \log \left (x+\left (x^2\right )^{2 (5+x)}\right )\right )^3}{x \left (1+x^{19} \left (x^2\right )^{2 x}\right )}\right ) \, dx}{e^9}\\ &=-\frac {4 \int \frac {\left (20+3 x+2 x \log \left (x^2\right )\right ) \left (-9+e^3 x-e^3 \log \left (x+\left (x^2\right )^{2 (5+x)}\right )\right )^3}{x} \, dx}{e^9}+\frac {4 \int \frac {\left (19+4 x+2 x \log \left (x^2\right )\right ) \left (-9+e^3 x-e^3 \log \left (x+\left (x^2\right )^{2 (5+x)}\right )\right )^3}{x \left (1+x^{19} \left (x^2\right )^{2 x}\right )} \, dx}{e^9}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [F] time = 1.23, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2916 x-2916 x^2+e^3 \left (-972 x^2+972 x^3\right )+e^6 \left (108 x^3-108 x^4\right )+e^9 \left (-4 x^4+4 x^5\right )+\left (x^2\right )^{10+2 x} \left (58320+8748 x+e^3 \left (-19440 x-2916 x^2\right )+e^6 \left (2160 x^2+324 x^3\right )+e^9 \left (-80 x^3-12 x^4\right )+\left (5832 x-1944 e^3 x^2+216 e^6 x^3-8 e^9 x^4\right ) \log \left (x^2\right )\right )+\left (e^3 \left (972 x-972 x^2\right )+e^6 \left (-216 x^2+216 x^3\right )+e^9 \left (12 x^3-12 x^4\right )+\left (x^2\right )^{10+2 x} \left (e^3 (19440+2916 x)+e^6 \left (-4320 x-648 x^2\right )+e^9 \left (240 x^2+36 x^3\right )+\left (1944 e^3 x-432 e^6 x^2+24 e^9 x^3\right ) \log \left (x^2\right )\right )\right ) \log \left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^6 \left (108 x-108 x^2\right )+e^9 \left (-12 x^2+12 x^3\right )+\left (x^2\right )^{10+2 x} \left (e^6 (2160+324 x)+e^9 \left (-240 x-36 x^2\right )+\left (216 e^6 x-24 e^9 x^2\right ) \log \left (x^2\right )\right )\right ) \log ^2\left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^9 \left (4 x-4 x^2\right )+\left (x^2\right )^{10+2 x} \left (e^9 (80+12 x)+8 e^9 x \log \left (x^2\right )\right )\right ) \log ^3\left (x+\left (x^2\right )^{10+2 x}\right )}{e^9 x^2+e^9 x \left (x^2\right )^{10+2 x}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Integrate[(2916*x - 2916*x^2 + E^3*(-972*x^2 + 972*x^3) + E^6*(108*x^3 - 108*x^4) + E^9*(-4*x^4 + 4*x^5) + (x^
2)^(10 + 2*x)*(58320 + 8748*x + E^3*(-19440*x - 2916*x^2) + E^6*(2160*x^2 + 324*x^3) + E^9*(-80*x^3 - 12*x^4)
+ (5832*x - 1944*E^3*x^2 + 216*E^6*x^3 - 8*E^9*x^4)*Log[x^2]) + (E^3*(972*x - 972*x^2) + E^6*(-216*x^2 + 216*x
^3) + E^9*(12*x^3 - 12*x^4) + (x^2)^(10 + 2*x)*(E^3*(19440 + 2916*x) + E^6*(-4320*x - 648*x^2) + E^9*(240*x^2
+ 36*x^3) + (1944*E^3*x - 432*E^6*x^2 + 24*E^9*x^3)*Log[x^2]))*Log[x + (x^2)^(10 + 2*x)] + (E^6*(108*x - 108*x
^2) + E^9*(-12*x^2 + 12*x^3) + (x^2)^(10 + 2*x)*(E^6*(2160 + 324*x) + E^9*(-240*x - 36*x^2) + (216*E^6*x - 24*
E^9*x^2)*Log[x^2]))*Log[x + (x^2)^(10 + 2*x)]^2 + (E^9*(4*x - 4*x^2) + (x^2)^(10 + 2*x)*(E^9*(80 + 12*x) + 8*E
^9*x*Log[x^2]))*Log[x + (x^2)^(10 + 2*x)]^3)/(E^9*x^2 + E^9*x*(x^2)^(10 + 2*x)),x]
[Out]
Integrate[(2916*x - 2916*x^2 + E^3*(-972*x^2 + 972*x^3) + E^6*(108*x^3 - 108*x^4) + E^9*(-4*x^4 + 4*x^5) + (x^
2)^(10 + 2*x)*(58320 + 8748*x + E^3*(-19440*x - 2916*x^2) + E^6*(2160*x^2 + 324*x^3) + E^9*(-80*x^3 - 12*x^4)
+ (5832*x - 1944*E^3*x^2 + 216*E^6*x^3 - 8*E^9*x^4)*Log[x^2]) + (E^3*(972*x - 972*x^2) + E^6*(-216*x^2 + 216*x
^3) + E^9*(12*x^3 - 12*x^4) + (x^2)^(10 + 2*x)*(E^3*(19440 + 2916*x) + E^6*(-4320*x - 648*x^2) + E^9*(240*x^2
+ 36*x^3) + (1944*E^3*x - 432*E^6*x^2 + 24*E^9*x^3)*Log[x^2]))*Log[x + (x^2)^(10 + 2*x)] + (E^6*(108*x - 108*x
^2) + E^9*(-12*x^2 + 12*x^3) + (x^2)^(10 + 2*x)*(E^6*(2160 + 324*x) + E^9*(-240*x - 36*x^2) + (216*E^6*x - 24*
E^9*x^2)*Log[x^2]))*Log[x + (x^2)^(10 + 2*x)]^2 + (E^9*(4*x - 4*x^2) + (x^2)^(10 + 2*x)*(E^9*(80 + 12*x) + 8*E
^9*x*Log[x^2]))*Log[x + (x^2)^(10 + 2*x)]^3)/(E^9*x^2 + E^9*x*(x^2)^(10 + 2*x)), x]
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fricas [B] time = 2.14, size = 135, normalized size = 5.87 \begin {gather*} {\left (x^{4} e^{9} + e^{9} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right )^{4} - 36 \, x^{3} e^{6} - 4 \, {\left (x e^{9} - 9 \, e^{6}\right )} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right )^{3} + 486 \, x^{2} e^{3} + 6 \, {\left (x^{2} e^{9} - 18 \, x e^{6} + 81 \, e^{3}\right )} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right )^{2} - 4 \, {\left (x^{3} e^{9} - 27 \, x^{2} e^{6} + 243 \, x e^{3} - 729\right )} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right ) - 2916 \, x\right )} e^{\left (-9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((8*x*exp(3)^3*log(x^2)+(12*x+80)*exp(3)^3)*exp((2*x+10)*log(x^2))+(-4*x^2+4*x)*exp(3)^3)*log(exp((
2*x+10)*log(x^2))+x)^3+(((-24*x^2*exp(3)^3+216*x*exp(3)^2)*log(x^2)+(-36*x^2-240*x)*exp(3)^3+(324*x+2160)*exp(
3)^2)*exp((2*x+10)*log(x^2))+(12*x^3-12*x^2)*exp(3)^3+(-108*x^2+108*x)*exp(3)^2)*log(exp((2*x+10)*log(x^2))+x)
^2+(((24*x^3*exp(3)^3-432*x^2*exp(3)^2+1944*x*exp(3))*log(x^2)+(36*x^3+240*x^2)*exp(3)^3+(-648*x^2-4320*x)*exp
(3)^2+(2916*x+19440)*exp(3))*exp((2*x+10)*log(x^2))+(-12*x^4+12*x^3)*exp(3)^3+(216*x^3-216*x^2)*exp(3)^2+(-972
*x^2+972*x)*exp(3))*log(exp((2*x+10)*log(x^2))+x)+((-8*x^4*exp(3)^3+216*x^3*exp(3)^2-1944*x^2*exp(3)+5832*x)*l
og(x^2)+(-12*x^4-80*x^3)*exp(3)^3+(324*x^3+2160*x^2)*exp(3)^2+(-2916*x^2-19440*x)*exp(3)+8748*x+58320)*exp((2*
x+10)*log(x^2))+(4*x^5-4*x^4)*exp(3)^3+(-108*x^4+108*x^3)*exp(3)^2+(972*x^3-972*x^2)*exp(3)-2916*x^2+2916*x)/(
x*exp(3)^3*exp((2*x+10)*log(x^2))+x^2*exp(3)^3),x, algorithm="fricas")
[Out]
(x^4*e^9 + e^9*log((x^2)^(2*x + 10) + x)^4 - 36*x^3*e^6 - 4*(x*e^9 - 9*e^6)*log((x^2)^(2*x + 10) + x)^3 + 486*
x^2*e^3 + 6*(x^2*e^9 - 18*x*e^6 + 81*e^3)*log((x^2)^(2*x + 10) + x)^2 - 4*(x^3*e^9 - 27*x^2*e^6 + 243*x*e^3 -
729)*log((x^2)^(2*x + 10) + x) - 2916*x)*e^(-9)
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((8*x*exp(3)^3*log(x^2)+(12*x+80)*exp(3)^3)*exp((2*x+10)*log(x^2))+(-4*x^2+4*x)*exp(3)^3)*log(exp((
2*x+10)*log(x^2))+x)^3+(((-24*x^2*exp(3)^3+216*x*exp(3)^2)*log(x^2)+(-36*x^2-240*x)*exp(3)^3+(324*x+2160)*exp(
3)^2)*exp((2*x+10)*log(x^2))+(12*x^3-12*x^2)*exp(3)^3+(-108*x^2+108*x)*exp(3)^2)*log(exp((2*x+10)*log(x^2))+x)
^2+(((24*x^3*exp(3)^3-432*x^2*exp(3)^2+1944*x*exp(3))*log(x^2)+(36*x^3+240*x^2)*exp(3)^3+(-648*x^2-4320*x)*exp
(3)^2+(2916*x+19440)*exp(3))*exp((2*x+10)*log(x^2))+(-12*x^4+12*x^3)*exp(3)^3+(216*x^3-216*x^2)*exp(3)^2+(-972
*x^2+972*x)*exp(3))*log(exp((2*x+10)*log(x^2))+x)+((-8*x^4*exp(3)^3+216*x^3*exp(3)^2-1944*x^2*exp(3)+5832*x)*l
og(x^2)+(-12*x^4-80*x^3)*exp(3)^3+(324*x^3+2160*x^2)*exp(3)^2+(-2916*x^2-19440*x)*exp(3)+8748*x+58320)*exp((2*
x+10)*log(x^2))+(4*x^5-4*x^4)*exp(3)^3+(-108*x^4+108*x^3)*exp(3)^2+(972*x^3-972*x^2)*exp(3)-2916*x^2+2916*x)/(
x*exp(3)^3*exp((2*x+10)*log(x^2))+x^2*exp(3)^3),x, algorithm="giac")
[Out]
Timed out
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maple [F] time = 0.65, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (8 x \,{\mathrm e}^{9} \ln \left (x^{2}\right )+\left (12 x +80\right ) {\mathrm e}^{9}\right ) {\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+\left (-4 x^{2}+4 x \right ) {\mathrm e}^{9}\right ) \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )^{3}+\left (\left (\left (-24 x^{2} {\mathrm e}^{9}+216 x \,{\mathrm e}^{6}\right ) \ln \left (x^{2}\right )+\left (-36 x^{2}-240 x \right ) {\mathrm e}^{9}+\left (324 x +2160\right ) {\mathrm e}^{6}\right ) {\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+\left (12 x^{3}-12 x^{2}\right ) {\mathrm e}^{9}+\left (-108 x^{2}+108 x \right ) {\mathrm e}^{6}\right ) \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )^{2}+\left (\left (\left (24 x^{3} {\mathrm e}^{9}-432 x^{2} {\mathrm e}^{6}+1944 x \,{\mathrm e}^{3}\right ) \ln \left (x^{2}\right )+\left (36 x^{3}+240 x^{2}\right ) {\mathrm e}^{9}+\left (-648 x^{2}-4320 x \right ) {\mathrm e}^{6}+\left (2916 x +19440\right ) {\mathrm e}^{3}\right ) {\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+\left (-12 x^{4}+12 x^{3}\right ) {\mathrm e}^{9}+\left (216 x^{3}-216 x^{2}\right ) {\mathrm e}^{6}+\left (-972 x^{2}+972 x \right ) {\mathrm e}^{3}\right ) \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )+\left (\left (-8 x^{4} {\mathrm e}^{9}+216 x^{3} {\mathrm e}^{6}-1944 x^{2} {\mathrm e}^{3}+5832 x \right ) \ln \left (x^{2}\right )+\left (-12 x^{4}-80 x^{3}\right ) {\mathrm e}^{9}+\left (324 x^{3}+2160 x^{2}\right ) {\mathrm e}^{6}+\left (-2916 x^{2}-19440 x \right ) {\mathrm e}^{3}+8748 x +58320\right ) {\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+\left (4 x^{5}-4 x^{4}\right ) {\mathrm e}^{9}+\left (-108 x^{4}+108 x^{3}\right ) {\mathrm e}^{6}+\left (972 x^{3}-972 x^{2}\right ) {\mathrm e}^{3}-2916 x^{2}+2916 x}{x \,{\mathrm e}^{9} {\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x^{2} {\mathrm e}^{9}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((8*x*exp(3)^3*ln(x^2)+(12*x+80)*exp(3)^3)*exp((2*x+10)*ln(x^2))+(-4*x^2+4*x)*exp(3)^3)*ln(exp((2*x+10)*l
n(x^2))+x)^3+(((-24*x^2*exp(3)^3+216*x*exp(3)^2)*ln(x^2)+(-36*x^2-240*x)*exp(3)^3+(324*x+2160)*exp(3)^2)*exp((
2*x+10)*ln(x^2))+(12*x^3-12*x^2)*exp(3)^3+(-108*x^2+108*x)*exp(3)^2)*ln(exp((2*x+10)*ln(x^2))+x)^2+(((24*x^3*e
xp(3)^3-432*x^2*exp(3)^2+1944*x*exp(3))*ln(x^2)+(36*x^3+240*x^2)*exp(3)^3+(-648*x^2-4320*x)*exp(3)^2+(2916*x+1
9440)*exp(3))*exp((2*x+10)*ln(x^2))+(-12*x^4+12*x^3)*exp(3)^3+(216*x^3-216*x^2)*exp(3)^2+(-972*x^2+972*x)*exp(
3))*ln(exp((2*x+10)*ln(x^2))+x)+((-8*x^4*exp(3)^3+216*x^3*exp(3)^2-1944*x^2*exp(3)+5832*x)*ln(x^2)+(-12*x^4-80
*x^3)*exp(3)^3+(324*x^3+2160*x^2)*exp(3)^2+(-2916*x^2-19440*x)*exp(3)+8748*x+58320)*exp((2*x+10)*ln(x^2))+(4*x
^5-4*x^4)*exp(3)^3+(-108*x^4+108*x^3)*exp(3)^2+(972*x^3-972*x^2)*exp(3)-2916*x^2+2916*x)/(x*exp(3)^3*exp((2*x+
10)*ln(x^2))+x^2*exp(3)^3),x)
[Out]
int((((8*x*exp(3)^3*ln(x^2)+(12*x+80)*exp(3)^3)*exp((2*x+10)*ln(x^2))+(-4*x^2+4*x)*exp(3)^3)*ln(exp((2*x+10)*l
n(x^2))+x)^3+(((-24*x^2*exp(3)^3+216*x*exp(3)^2)*ln(x^2)+(-36*x^2-240*x)*exp(3)^3+(324*x+2160)*exp(3)^2)*exp((
2*x+10)*ln(x^2))+(12*x^3-12*x^2)*exp(3)^3+(-108*x^2+108*x)*exp(3)^2)*ln(exp((2*x+10)*ln(x^2))+x)^2+(((24*x^3*e
xp(3)^3-432*x^2*exp(3)^2+1944*x*exp(3))*ln(x^2)+(36*x^3+240*x^2)*exp(3)^3+(-648*x^2-4320*x)*exp(3)^2+(2916*x+1
9440)*exp(3))*exp((2*x+10)*ln(x^2))+(-12*x^4+12*x^3)*exp(3)^3+(216*x^3-216*x^2)*exp(3)^2+(-972*x^2+972*x)*exp(
3))*ln(exp((2*x+10)*ln(x^2))+x)+((-8*x^4*exp(3)^3+216*x^3*exp(3)^2-1944*x^2*exp(3)+5832*x)*ln(x^2)+(-12*x^4-80
*x^3)*exp(3)^3+(324*x^3+2160*x^2)*exp(3)^2+(-2916*x^2-19440*x)*exp(3)+8748*x+58320)*exp((2*x+10)*ln(x^2))+(4*x
^5-4*x^4)*exp(3)^3+(-108*x^4+108*x^3)*exp(3)^2+(972*x^3-972*x^2)*exp(3)-2916*x^2+2916*x)/(x*exp(3)^3*exp((2*x+
10)*ln(x^2))+x^2*exp(3)^3),x)
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 4 \, \int \frac {{\left ({\left (2 \, x e^{9} \log \left (x^{2}\right ) + {\left (3 \, x + 20\right )} e^{9}\right )} {\left (x^{2}\right )}^{2 \, x + 10} - {\left (x^{2} - x\right )} e^{9}\right )} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right )^{3} - 3 \, {\left ({\left ({\left (3 \, x^{2} + 20 \, x\right )} e^{9} - 9 \, {\left (3 \, x + 20\right )} e^{6} + 2 \, {\left (x^{2} e^{9} - 9 \, x e^{6}\right )} \log \left (x^{2}\right )\right )} {\left (x^{2}\right )}^{2 \, x + 10} - {\left (x^{3} - x^{2}\right )} e^{9} + 9 \, {\left (x^{2} - x\right )} e^{6}\right )} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right )^{2} - {\left ({\left (3 \, x^{4} + 20 \, x^{3}\right )} e^{9} - 27 \, {\left (3 \, x^{3} + 20 \, x^{2}\right )} e^{6} + 243 \, {\left (3 \, x^{2} + 20 \, x\right )} e^{3} + 2 \, {\left (x^{4} e^{9} - 27 \, x^{3} e^{6} + 243 \, x^{2} e^{3} - 729 \, x\right )} \log \left (x^{2}\right ) - 2187 \, x - 14580\right )} {\left (x^{2}\right )}^{2 \, x + 10} - 729 \, x^{2} + {\left (x^{5} - x^{4}\right )} e^{9} - 27 \, {\left (x^{4} - x^{3}\right )} e^{6} + 243 \, {\left (x^{3} - x^{2}\right )} e^{3} + 3 \, {\left ({\left ({\left (3 \, x^{3} + 20 \, x^{2}\right )} e^{9} - 18 \, {\left (3 \, x^{2} + 20 \, x\right )} e^{6} + 81 \, {\left (3 \, x + 20\right )} e^{3} + 2 \, {\left (x^{3} e^{9} - 18 \, x^{2} e^{6} + 81 \, x e^{3}\right )} \log \left (x^{2}\right )\right )} {\left (x^{2}\right )}^{2 \, x + 10} - {\left (x^{4} - x^{3}\right )} e^{9} + 18 \, {\left (x^{3} - x^{2}\right )} e^{6} - 81 \, {\left (x^{2} - x\right )} e^{3}\right )} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right ) + 729 \, x}{{\left (x^{2}\right )}^{2 \, x + 10} x e^{9} + x^{2} e^{9}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((8*x*exp(3)^3*log(x^2)+(12*x+80)*exp(3)^3)*exp((2*x+10)*log(x^2))+(-4*x^2+4*x)*exp(3)^3)*log(exp((
2*x+10)*log(x^2))+x)^3+(((-24*x^2*exp(3)^3+216*x*exp(3)^2)*log(x^2)+(-36*x^2-240*x)*exp(3)^3+(324*x+2160)*exp(
3)^2)*exp((2*x+10)*log(x^2))+(12*x^3-12*x^2)*exp(3)^3+(-108*x^2+108*x)*exp(3)^2)*log(exp((2*x+10)*log(x^2))+x)
^2+(((24*x^3*exp(3)^3-432*x^2*exp(3)^2+1944*x*exp(3))*log(x^2)+(36*x^3+240*x^2)*exp(3)^3+(-648*x^2-4320*x)*exp
(3)^2+(2916*x+19440)*exp(3))*exp((2*x+10)*log(x^2))+(-12*x^4+12*x^3)*exp(3)^3+(216*x^3-216*x^2)*exp(3)^2+(-972
*x^2+972*x)*exp(3))*log(exp((2*x+10)*log(x^2))+x)+((-8*x^4*exp(3)^3+216*x^3*exp(3)^2-1944*x^2*exp(3)+5832*x)*l
og(x^2)+(-12*x^4-80*x^3)*exp(3)^3+(324*x^3+2160*x^2)*exp(3)^2+(-2916*x^2-19440*x)*exp(3)+8748*x+58320)*exp((2*
x+10)*log(x^2))+(4*x^5-4*x^4)*exp(3)^3+(-108*x^4+108*x^3)*exp(3)^2+(972*x^3-972*x^2)*exp(3)-2916*x^2+2916*x)/(
x*exp(3)^3*exp((2*x+10)*log(x^2))+x^2*exp(3)^3),x, algorithm="maxima")
[Out]
4*integrate((((2*x*e^9*log(x^2) + (3*x + 20)*e^9)*(x^2)^(2*x + 10) - (x^2 - x)*e^9)*log((x^2)^(2*x + 10) + x)^
3 - 3*(((3*x^2 + 20*x)*e^9 - 9*(3*x + 20)*e^6 + 2*(x^2*e^9 - 9*x*e^6)*log(x^2))*(x^2)^(2*x + 10) - (x^3 - x^2)
*e^9 + 9*(x^2 - x)*e^6)*log((x^2)^(2*x + 10) + x)^2 - ((3*x^4 + 20*x^3)*e^9 - 27*(3*x^3 + 20*x^2)*e^6 + 243*(3
*x^2 + 20*x)*e^3 + 2*(x^4*e^9 - 27*x^3*e^6 + 243*x^2*e^3 - 729*x)*log(x^2) - 2187*x - 14580)*(x^2)^(2*x + 10)
- 729*x^2 + (x^5 - x^4)*e^9 - 27*(x^4 - x^3)*e^6 + 243*(x^3 - x^2)*e^3 + 3*(((3*x^3 + 20*x^2)*e^9 - 18*(3*x^2
+ 20*x)*e^6 + 81*(3*x + 20)*e^3 + 2*(x^3*e^9 - 18*x^2*e^6 + 81*x*e^3)*log(x^2))*(x^2)^(2*x + 10) - (x^4 - x^3)
*e^9 + 18*(x^3 - x^2)*e^6 - 81*(x^2 - x)*e^3)*log((x^2)^(2*x + 10) + x) + 729*x)/((x^2)^(2*x + 10)*x*e^9 + x^2
*e^9), x)
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mupad [B] time = 6.34, size = 178, normalized size = 7.74 \begin {gather*} 2916\,{\mathrm {e}}^{-9}\,\ln \left (x+x^{20}\,{\left (x^2\right )}^{2\,x}\right )-{\ln \left (x+x^{20}\,{\left (x^2\right )}^{2\,x}\right )}^3\,\left (4\,x-36\,{\mathrm {e}}^{-3}\right )-2916\,x\,{\mathrm {e}}^{-9}+{\ln \left (x+x^{20}\,{\left (x^2\right )}^{2\,x}\right )}^2\,\left (486\,{\mathrm {e}}^{-6}-432\,x\,{\mathrm {e}}^{-3}+\frac {{\mathrm {e}}^{-3}\,\left (6\,{\mathrm {e}}^3\,x^3+324\,x^2\right )}{x}\right )-36\,x^3\,{\mathrm {e}}^{-3}+486\,x^2\,{\mathrm {e}}^{-6}+x^4+{\ln \left (x+x^{20}\,{\left (x^2\right )}^{2\,x}\right )}^4-\ln \left (x+x^{20}\,{\left (x^2\right )}^{2\,x}\right )\,\left (3888\,x\,{\mathrm {e}}^{-6}-\frac {{\mathrm {e}}^{-6}\,\left (-4\,{\mathrm {e}}^6\,x^4+108\,{\mathrm {e}}^3\,x^3+2916\,x^2\right )}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((2916*x + log(x + exp(log(x^2)*(2*x + 10)))^3*(exp(9)*(4*x - 4*x^2) + exp(log(x^2)*(2*x + 10))*(exp(9)*(12
*x + 80) + 8*x*log(x^2)*exp(9))) + log(x + exp(log(x^2)*(2*x + 10)))^2*(exp(log(x^2)*(2*x + 10))*(log(x^2)*(21
6*x*exp(6) - 24*x^2*exp(9)) - exp(9)*(240*x + 36*x^2) + exp(6)*(324*x + 2160)) + exp(6)*(108*x - 108*x^2) - ex
p(9)*(12*x^2 - 12*x^3)) - exp(9)*(4*x^4 - 4*x^5) + exp(6)*(108*x^3 - 108*x^4) - exp(3)*(972*x^2 - 972*x^3) + l
og(x + exp(log(x^2)*(2*x + 10)))*(exp(3)*(972*x - 972*x^2) + exp(log(x^2)*(2*x + 10))*(log(x^2)*(1944*x*exp(3)
- 432*x^2*exp(6) + 24*x^3*exp(9)) - exp(6)*(4320*x + 648*x^2) + exp(9)*(240*x^2 + 36*x^3) + exp(3)*(2916*x +
19440)) + exp(9)*(12*x^3 - 12*x^4) - exp(6)*(216*x^2 - 216*x^3)) - 2916*x^2 + exp(log(x^2)*(2*x + 10))*(8748*x
- exp(3)*(19440*x + 2916*x^2) - exp(9)*(80*x^3 + 12*x^4) + exp(6)*(2160*x^2 + 324*x^3) + log(x^2)*(5832*x - 1
944*x^2*exp(3) + 216*x^3*exp(6) - 8*x^4*exp(9)) + 58320))/(x^2*exp(9) + x*exp(log(x^2)*(2*x + 10))*exp(9)),x)
[Out]
2916*exp(-9)*log(x + x^20*(x^2)^(2*x)) - log(x + x^20*(x^2)^(2*x))^3*(4*x - 36*exp(-3)) - 2916*x*exp(-9) + log
(x + x^20*(x^2)^(2*x))^2*(486*exp(-6) - 432*x*exp(-3) + (exp(-3)*(6*x^3*exp(3) + 324*x^2))/x) - 36*x^3*exp(-3)
+ 486*x^2*exp(-6) + x^4 + log(x + x^20*(x^2)^(2*x))^4 - log(x + x^20*(x^2)^(2*x))*(3888*x*exp(-6) - (exp(-6)*
(108*x^3*exp(3) - 4*x^4*exp(6) + 2916*x^2))/x)
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sympy [B] time = 2.03, size = 168, normalized size = 7.30 \begin {gather*} x^{4} - \frac {36 x^{3}}{e^{3}} + \frac {486 x^{2}}{e^{6}} - \frac {2916 x}{e^{9}} + \frac {\left (- 4 x e^{3} + 36\right ) \log {\left (x + e^{\left (2 x + 10\right ) \log {\left (x^{2} \right )}} \right )}^{3}}{e^{3}} + \frac {\left (6 x^{2} e^{6} - 108 x e^{3} + 486\right ) \log {\left (x + e^{\left (2 x + 10\right ) \log {\left (x^{2} \right )}} \right )}^{2}}{e^{6}} + \frac {\left (- 4 x^{3} e^{6} + 108 x^{2} e^{3} - 972 x\right ) \log {\left (x + e^{\left (2 x + 10\right ) \log {\left (x^{2} \right )}} \right )}}{e^{6}} + \log {\left (x + e^{\left (2 x + 10\right ) \log {\left (x^{2} \right )}} \right )}^{4} + \frac {2916 \log {\left (x + e^{\left (2 x + 10\right ) \log {\left (x^{2} \right )}} \right )}}{e^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((8*x*exp(3)**3*ln(x**2)+(12*x+80)*exp(3)**3)*exp((2*x+10)*ln(x**2))+(-4*x**2+4*x)*exp(3)**3)*ln(ex
p((2*x+10)*ln(x**2))+x)**3+(((-24*x**2*exp(3)**3+216*x*exp(3)**2)*ln(x**2)+(-36*x**2-240*x)*exp(3)**3+(324*x+2
160)*exp(3)**2)*exp((2*x+10)*ln(x**2))+(12*x**3-12*x**2)*exp(3)**3+(-108*x**2+108*x)*exp(3)**2)*ln(exp((2*x+10
)*ln(x**2))+x)**2+(((24*x**3*exp(3)**3-432*x**2*exp(3)**2+1944*x*exp(3))*ln(x**2)+(36*x**3+240*x**2)*exp(3)**3
+(-648*x**2-4320*x)*exp(3)**2+(2916*x+19440)*exp(3))*exp((2*x+10)*ln(x**2))+(-12*x**4+12*x**3)*exp(3)**3+(216*
x**3-216*x**2)*exp(3)**2+(-972*x**2+972*x)*exp(3))*ln(exp((2*x+10)*ln(x**2))+x)+((-8*x**4*exp(3)**3+216*x**3*e
xp(3)**2-1944*x**2*exp(3)+5832*x)*ln(x**2)+(-12*x**4-80*x**3)*exp(3)**3+(324*x**3+2160*x**2)*exp(3)**2+(-2916*
x**2-19440*x)*exp(3)+8748*x+58320)*exp((2*x+10)*ln(x**2))+(4*x**5-4*x**4)*exp(3)**3+(-108*x**4+108*x**3)*exp(3
)**2+(972*x**3-972*x**2)*exp(3)-2916*x**2+2916*x)/(x*exp(3)**3*exp((2*x+10)*ln(x**2))+x**2*exp(3)**3),x)
[Out]
x**4 - 36*x**3*exp(-3) + 486*x**2*exp(-6) - 2916*x*exp(-9) + (-4*x*exp(3) + 36)*exp(-3)*log(x + exp((2*x + 10)
*log(x**2)))**3 + (6*x**2*exp(6) - 108*x*exp(3) + 486)*exp(-6)*log(x + exp((2*x + 10)*log(x**2)))**2 + (-4*x**
3*exp(6) + 108*x**2*exp(3) - 972*x)*exp(-6)*log(x + exp((2*x + 10)*log(x**2))) + log(x + exp((2*x + 10)*log(x*
*2)))**4 + 2916*exp(-9)*log(x + exp((2*x + 10)*log(x**2)))
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