43.24 Problem number 2955

$$\int \frac{e^{\frac{6561+5832x^2-2916x^3+1944x^4-1944x^5+774x^6-432x^7+232x^8+e^4{x}^8+e^5{x}^8-68x^9+24x^{10}-8x^{11}+x^{12}+e^2(162x^4+72x^6-36x^7+8x^8-8x^9+2x^{10})+(-2916x^2-1944x^4+972x^5-432x^6+432x^7-140x^8+48x^9-24x^{10}+4x^{11}+e^2(-36x^6-8x^8+4x^9))\log (x)+(486x^4+216x^6-108x^7+24x^8+2e^2{x}^8-24x^9+6x^{10}){\log }^2(x)+(-36x^6-8x^8+4x^9){\log }^3(x)+x^8{\log }^4(x)}{x^8}}(-52488-37908x^2+14580x^3-9720x^4+6804x^5-1980x^6+864x^7-140x^8-20x^9+24x^{10}-20x^{11}+4x^{12}+e^2(-648x^4-180x^6+36x^7-8x^8-4x^9+4x^{10})+(17496x^2+8748x^4-2916x^5+1296x^6-648x^7+48x^8-36x^{10}+12x^{11}+e^2(72x^6+4x^8+4x^9))\log (x)+(-1944x^4-540x^6+108x^7-24x^8-12x^9+12x^{10}){\log }^2(x)+(72x^6+4x^8+4x^9){\log }^3(x))}{x^9}dx$$

Optimal antiderivative $${\mathrm{e}}^{{({\mathrm{e}}^2+{(\frac{9}{x^2}-\ln \left(x\right)+2-x)}^2)}^2+{\mathrm{e}}^5}-1$$

command

integrate(((4*x^9+4*x^8+72*x^6)*log(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-540*x^6-1944*x^4)*log(x)^2+((4*x^9+4*x^8+72*x^6)*exp(2)+12*x^11-36*x^10+48*x^8-648*x^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*log(x)+(4*x^10-4*x^9-8*x^8+36*x^7-180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864*x^7-1980*x^6+6804*x^5-9720*x^4+14580*x^3-37908*x^2-52488)*exp((x^8*log(x)^4+(4*x^9-8*x^8-36*x^6)*log(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-108*x^7+216*x^6+486*x^4)*log(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48*x^9-140*x^8+432*x^7-432*x^6+972*x^5-1944*x^4-2916*x^2)*log(x)+x^8*exp(5)+x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-8*x^11+24*x^10-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^2+6561)/x^8)/x^9,x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

$$\text{could not integrate}$$

Giac 1.7.0 via sagemath 9.3 output

$$e^{(x^4+4x^3\log \left(x\right)+6x^2\log {\left(x\right)}^2+4x\log {\left(x\right)}^3+\log {\left(x\right)}^4-8x^3+2x^2{e}^2-24x^2\log \left(x\right)+4x{e}^2\log \left(x\right)-24x\log {\left(x\right)}^2+2e^2\log {\left(x\right)}^2-8\log {\left(x\right)}^3+24x^2-8x{e}^2+48x\log \left(x\right)-8e^2\log \left(x\right)+24\log {\left(x\right)}^2-68x-\frac{108\log {\left(x\right)}^2}{x}-\frac{36\log {\left(x\right)}^3}{x^2}-\frac{36e^2}{x}+\frac{432\log \left(x\right)}{x}-\frac{36e^2\log \left(x\right)}{x^2}+\frac{216\log {\left(x\right)}^2}{x^2}-\frac{432}{x}+\frac{72e^2}{x^2}-\frac{432\log \left(x\right)}{x^2}+\frac{774}{x^2}+\frac{972\log \left(x\right)}{x^3}+\frac{486\log {\left(x\right)}^2}{x^4}-\frac{1944}{x^3}+\frac{162e^2}{x^4}-\frac{1944\log \left(x\right)}{x^4}+\frac{1944}{x^4}-\frac{2916}{x^5}-\frac{2916\log \left(x\right)}{x^6}+\frac{5832}{x^6}+\frac{6561}{x^8}+e^5+e^4+8e^2-140\log \left(x\right)+232)}$$