Integrand size = 459, antiderivative size = 23 \[ \int \frac {2916 x-2916 x^2+e^3 \left (-972 x^2+972 x^3\right )+e^6 \left (108 x^3-108 x^4\right )+e^9 \left (-4 x^4+4 x^5\right )+\left (x^2\right )^{10+2 x} \left (58320+8748 x+e^3 \left (-19440 x-2916 x^2\right )+e^6 \left (2160 x^2+324 x^3\right )+e^9 \left (-80 x^3-12 x^4\right )+\left (5832 x-1944 e^3 x^2+216 e^6 x^3-8 e^9 x^4\right ) \log \left (x^2\right )\right )+\left (e^3 \left (972 x-972 x^2\right )+e^6 \left (-216 x^2+216 x^3\right )+e^9 \left (12 x^3-12 x^4\right )+\left (x^2\right )^{10+2 x} \left (e^3 (19440+2916 x)+e^6 \left (-4320 x-648 x^2\right )+e^9 \left (240 x^2+36 x^3\right )+\left (1944 e^3 x-432 e^6 x^2+24 e^9 x^3\right ) \log \left (x^2\right )\right )\right ) \log \left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^6 \left (108 x-108 x^2\right )+e^9 \left (-12 x^2+12 x^3\right )+\left (x^2\right )^{10+2 x} \left (e^6 (2160+324 x)+e^9 \left (-240 x-36 x^2\right )+\left (216 e^6 x-24 e^9 x^2\right ) \log \left (x^2\right )\right )\right ) \log ^2\left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^9 \left (4 x-4 x^2\right )+\left (x^2\right )^{10+2 x} \left (e^9 (80+12 x)+8 e^9 x \log \left (x^2\right )\right )\right ) \log ^3\left (x+\left (x^2\right )^{10+2 x}\right )}{e^9 x^2+e^9 x \left (x^2\right )^{10+2 x}} \, dx=\left (-\frac {9}{e^3}+x-\log \left (x+\left (x^2\right )^{2 (5+x)}\right )\right )^4 \]
\[ \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=\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 \]
Integrate[(2916*x - 2916*x^2 + E^3*(-972*x^2 + 972*x^3) + E^6*(108*x^3 - 1 08*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]
Integrate[(2916*x - 2916*x^2 + E^3*(-972*x^2 + 972*x^3) + E^6*(108*x^3 - 1 08*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]
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.
| \(\displaystyle \int \frac {-2916 x^2+\left (e^9 \left (4 x-4 x^2\right )+\left (x^2\right )^{2 x+10} \left (8 e^9 x \log \left (x^2\right )+e^9 (12 x+80)\right )\right ) \log ^3\left (\left (x^2\right )^{2 x+10}+x\right )+e^9 \left (4 x^5-4 x^4\right )+e^6 \left (108 x^3-108 x^4\right )+e^3 \left (972 x^3-972 x^2\right )+\left (e^6 \left (108 x-108 x^2\right )+\left (x^2\right )^{2 x+10} \left (e^9 \left (-36 x^2-240 x\right )+\left (216 e^6 x-24 e^9 x^2\right ) \log \left (x^2\right )+e^6 (324 x+2160)\right )+e^9 \left (12 x^3-12 x^2\right )\right ) \log ^2\left (\left (x^2\right )^{2 x+10}+x\right )+\left (x^2\right )^{2 x+10} \left (e^3 \left (-2916 x^2-19440 x\right )+e^9 \left (-12 x^4-80 x^3\right )+e^6 \left (324 x^3+2160 x^2\right )+\left (-8 e^9 x^4+216 e^6 x^3-1944 e^3 x^2+5832 x\right ) \log \left (x^2\right )+8748 x+58320\right )+\left (e^3 \left (972 x-972 x^2\right )+e^9 \left (12 x^3-12 x^4\right )+e^6 \left (216 x^3-216 x^2\right )+\left (x^2\right )^{2 x+10} \left (e^6 \left (-648 x^2-4320 x\right )+e^9 \left (36 x^3+240 x^2\right )+\left (24 e^9 x^3-432 e^6 x^2+1944 e^3 x\right ) \log \left (x^2\right )+e^3 (2916 x+19440)\right )\right ) \log \left (\left (x^2\right )^{2 x+10}+x\right )+2916 x}{e^9 x \left (x^2\right )^{2 x+10}+e^9 x^2} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (3 x^{20} \left (x^2\right )^{2 x}+2 x^{20} \left (x^2\right )^{2 x} \log \left (x^2\right )+20 x^{19} \left (x^2\right )^{2 x}-x+1\right ) \left (e^3 \log \left (\left (x^2\right )^{2 (x+5)}+x\right )-e^3 x+9\right )^3}{e^9 \left (x^{20} \left (x^2\right )^{2 x}+x\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {4 \int \frac {\left (3 x^{20} \left (x^2\right )^{2 x}+20 x^{19} \left (x^2\right )^{2 x}+2 x^{20} \log \left (x^2\right ) \left (x^2\right )^{2 x}-x+1\right ) \left (-e^3 x+e^3 \log \left (\left (x^2\right )^{2 (x+5)}+x\right )+9\right )^3}{x^{20} \left (x^2\right )^{2 x}+x}dx}{e^9}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {4 \int \left (\frac {\left (2 \log \left (x^2\right ) x+4 x+19\right ) \left (e^3 x-e^3 \log \left (\left (x^2\right )^{2 (x+5)}+x\right )-9\right )^3}{x \left (x^{19} \left (x^2\right )^{2 x}+1\right )}-\frac {\left (2 \log \left (x^2\right ) x+3 x+20\right ) \left (e^3 x-e^3 \log \left (\left (x^2\right )^{2 (x+5)}+x\right )-9\right )^3}{x}\right )dx}{e^9}\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \frac {4 \int \left (\frac {\left (2 \log \left (x^2\right ) x+4 x+19\right ) \left (e^3 x-e^3 \log \left (\left (x^2\right )^{2 (x+5)}+x\right )-9\right )^3}{x \left (x^{19} \left (x^2\right )^{2 x}+1\right )}-\frac {\left (2 \log \left (x^2\right ) x+3 x+20\right ) \left (e^3 x-e^3 \log \left (\left (x^2\right )^{2 (x+5)}+x\right )-9\right )^3}{x}\right )dx}{e^9}\) |
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) + (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]
3.26.60.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(251\) vs. \(2(25)=50\).
Time = 11.45 (sec) , antiderivative size = 252, normalized size of antiderivative = 10.96
| method | result | size |
| parallelrisch | \(\frac {\left (2 x^{4} {\mathrm e}^{9}-8 \,{\mathrm e}^{9} \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right ) x^{3}+12 \,{\mathrm e}^{9} \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )^{2} x^{2}-8 \,{\mathrm e}^{9} x \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )^{3}+2 \,{\mathrm e}^{9} \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )^{4}-72 x^{3} {\mathrm e}^{6}+216 \,{\mathrm e}^{6} \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right ) x^{2}-216 \,{\mathrm e}^{6} \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )^{2} x +72 \,{\mathrm e}^{6} \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )^{3}+972 x^{2} {\mathrm e}^{3}-1944 \,{\mathrm e}^{3} \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right ) x +972 \,{\mathrm e}^{3} \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )^{2}-5832 x +5832 \ln \left ({\mathrm e}^{\left (2 x +10\right ) \ln \left (x^{2}\right )}+x \right )\right ) {\mathrm e}^{-9}}{2}\) | \(252\) |
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)*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+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*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*e xp(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+583 20)*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,method=_RETURNVERBOSE)
1/2*(2*x^4*exp(3)^3-8*exp(3)^3*ln(exp((2*x+10)*ln(x^2))+x)*x^3+12*exp(3)^3 *ln(exp((2*x+10)*ln(x^2))+x)^2*x^2-8*x*exp(3)^3*ln(exp((2*x+10)*ln(x^2))+x )^3+2*exp(3)^3*ln(exp((2*x+10)*ln(x^2))+x)^4-72*x^3*exp(3)^2+216*exp(3)^2* ln(exp((2*x+10)*ln(x^2))+x)*x^2-216*exp(3)^2*ln(exp((2*x+10)*ln(x^2))+x)^2 *x+72*exp(3)^2*ln(exp((2*x+10)*ln(x^2))+x)^3+972*x^2*exp(3)-1944*exp(3)*ln (exp((2*x+10)*ln(x^2))+x)*x+972*exp(3)*ln(exp((2*x+10)*ln(x^2))+x)^2-5832* x+5832*ln(exp((2*x+10)*ln(x^2))+x))/exp(3)^3
Leaf count of result is larger than twice the leaf count of optimal. 135 vs. \(2 (22) = 44\).
Time = 0.27 (sec) , antiderivative size = 135, normalized size of antiderivative = 5.87 \[ \int \frac {2916 x-2916 x^2+e^3 \left (-972 x^2+972 x^3\right )+e^6 \left (108 x^3-108 x^4\right )+e^9 \left (-4 x^4+4 x^5\right )+\left (x^2\right )^{10+2 x} \left (58320+8748 x+e^3 \left (-19440 x-2916 x^2\right )+e^6 \left (2160 x^2+324 x^3\right )+e^9 \left (-80 x^3-12 x^4\right )+\left (5832 x-1944 e^3 x^2+216 e^6 x^3-8 e^9 x^4\right ) \log \left (x^2\right )\right )+\left (e^3 \left (972 x-972 x^2\right )+e^6 \left (-216 x^2+216 x^3\right )+e^9 \left (12 x^3-12 x^4\right )+\left (x^2\right )^{10+2 x} \left (e^3 (19440+2916 x)+e^6 \left (-4320 x-648 x^2\right )+e^9 \left (240 x^2+36 x^3\right )+\left (1944 e^3 x-432 e^6 x^2+24 e^9 x^3\right ) \log \left (x^2\right )\right )\right ) \log \left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^6 \left (108 x-108 x^2\right )+e^9 \left (-12 x^2+12 x^3\right )+\left (x^2\right )^{10+2 x} \left (e^6 (2160+324 x)+e^9 \left (-240 x-36 x^2\right )+\left (216 e^6 x-24 e^9 x^2\right ) \log \left (x^2\right )\right )\right ) \log ^2\left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^9 \left (4 x-4 x^2\right )+\left (x^2\right )^{10+2 x} \left (e^9 (80+12 x)+8 e^9 x \log \left (x^2\right )\right )\right ) \log ^3\left (x+\left (x^2\right )^{10+2 x}\right )}{e^9 x^2+e^9 x \left (x^2\right )^{10+2 x}} \, dx={\left (x^{4} e^{9} + e^{9} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right )^{4} - 36 \, x^{3} e^{6} - 4 \, {\left (x e^{9} - 9 \, e^{6}\right )} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right )^{3} + 486 \, x^{2} e^{3} + 6 \, {\left (x^{2} e^{9} - 18 \, x e^{6} + 81 \, e^{3}\right )} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right )^{2} - 4 \, {\left (x^{3} e^{9} - 27 \, x^{2} e^{6} + 243 \, x e^{3} - 729\right )} \log \left ({\left (x^{2}\right )}^{2 \, x + 10} + x\right ) - 2916 \, x\right )} e^{\left (-9\right )} \]
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+1 944*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)*log(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=\
(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 - 72 9)*log((x^2)^(2*x + 10) + x) - 2916*x)*e^(-9)
Leaf count of result is larger than twice the leaf count of optimal. 168 vs. \(2 (22) = 44\).
Time = 0.97 (sec) , antiderivative size = 168, normalized size of antiderivative = 7.30 \[ \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=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}} \]
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(exp((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+216 0)*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)**3-4 32*x**2*exp(3)**2+1944*x*exp(3))*ln(x**2)+(36*x**3+240*x**2)*exp(3)**3+(-6 48*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*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+(97 2*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)
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)))
\[ \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=\int { \frac {4 \, {\left ({\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\right )}}{{\left (x^{2}\right )}^{2 \, x + 10} x e^{9} + x^{2} e^{9}} \,d x } \]
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+1 944*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)*log(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=\
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) - 72 9*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)
Timed out. \[ \int \frac {2916 x-2916 x^2+e^3 \left (-972 x^2+972 x^3\right )+e^6 \left (108 x^3-108 x^4\right )+e^9 \left (-4 x^4+4 x^5\right )+\left (x^2\right )^{10+2 x} \left (58320+8748 x+e^3 \left (-19440 x-2916 x^2\right )+e^6 \left (2160 x^2+324 x^3\right )+e^9 \left (-80 x^3-12 x^4\right )+\left (5832 x-1944 e^3 x^2+216 e^6 x^3-8 e^9 x^4\right ) \log \left (x^2\right )\right )+\left (e^3 \left (972 x-972 x^2\right )+e^6 \left (-216 x^2+216 x^3\right )+e^9 \left (12 x^3-12 x^4\right )+\left (x^2\right )^{10+2 x} \left (e^3 (19440+2916 x)+e^6 \left (-4320 x-648 x^2\right )+e^9 \left (240 x^2+36 x^3\right )+\left (1944 e^3 x-432 e^6 x^2+24 e^9 x^3\right ) \log \left (x^2\right )\right )\right ) \log \left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^6 \left (108 x-108 x^2\right )+e^9 \left (-12 x^2+12 x^3\right )+\left (x^2\right )^{10+2 x} \left (e^6 (2160+324 x)+e^9 \left (-240 x-36 x^2\right )+\left (216 e^6 x-24 e^9 x^2\right ) \log \left (x^2\right )\right )\right ) \log ^2\left (x+\left (x^2\right )^{10+2 x}\right )+\left (e^9 \left (4 x-4 x^2\right )+\left (x^2\right )^{10+2 x} \left (e^9 (80+12 x)+8 e^9 x \log \left (x^2\right )\right )\right ) \log ^3\left (x+\left (x^2\right )^{10+2 x}\right )}{e^9 x^2+e^9 x \left (x^2\right )^{10+2 x}} \, dx=\text {Timed out} \]
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+1 944*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)*log(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=\
Time = 15.09 (sec) , antiderivative size = 178, normalized size of antiderivative = 7.74 \[ \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=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 ) \]
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)*(216* 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) - exp(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) + log(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 + ex p(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 - 1944*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)
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)