43.17 Problem number 2306

$$\int \frac{e^{16x^8}(-839808-209952x)+e^{16x^8}(10917504x^7+6718464x^8+839808x^9)\log (13+8x+x^2)+e^{12x^8}(279936+69984x){\log }^4(13+8x+x^2)+e^{12x^8}(-3639168x^7-2239488x^8-279936x^9){\log }^5(13+8x+x^2)+e^{8x^8}(-31104-7776x){\log }^8(13+8x+x^2)+e^{8x^8}(404352x^7+248832x^8+31104x^9){\log }^9(13+8x+x^2)+e^{4x^8}(1152+288x){\log }^{12}(13+8x+x^2)+e^{4x^8}(-14976x^7-9216x^8-1152x^9){\log }^{13}(13+8x+x^2)}{(13+8x+x^2){\log }^{17}(13+8x+x^2)}dx$$

Optimal antiderivative $${(\frac{9{\mathrm{e}}^{4x^8}}{\ln {({(4+x)}^2-3)}^4}-1)}^4$$

command

integrate(((-1152*x^9-9216*x^8-14976*x^7)*exp(x^8)^4*log(x^2+8*x+13)^13+(288*x+1152)*exp(x^8)^4*log(x^2+8*x+13)^12+(31104*x^9+248832*x^8+404352*x^7)*exp(x^8)^8*log(x^2+8*x+13)^9+(-7776*x-31104)*exp(x^8)^8*log(x^2+8*x+13)^8+(-279936*x^9-2239488*x^8-3639168*x^7)*exp(x^8)^12*log(x^2+8*x+13)^5+(69984*x+279936)*exp(x^8)^12*log(x^2+8*x+13)^4+(839808*x^9+6718464*x^8+10917504*x^7)*exp(x^8)^16*log(x^2+8*x+13)+(-209952*x-839808)*exp(x^8)^16)/(x^2+8*x+13)/log(x^2+8*x+13)^17,x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

$$\text{Timed out}$$

Giac 1.7.0 via sagemath 9.3 output

$$-\frac{9(4e^{\left(4x^8\right)}\log {(x^2+8x+13)}^{12}-54e^{\left(8x^8\right)}\log {(x^2+8x+13)}^8+324e^{\left(12x^8\right)}\log {(x^2+8x+13)}^4-729e^{\left(16x^8\right)})}{\log {(x^2+8x+13)}^{16}}$$