43.32 Problem number 4209

\[ \int \frac {e^{\frac {2 \left (-e^6+x+4 e^3 x-4 x^2+\left (2+e^6-x-4 e^3 x+4 x^2+\left (e^6 x-x^2-4 e^3 x^2+4 x^3\right ) \log (4)\right ) \log (x)\right )}{-1+(1+x \log (4)) \log (x)}} \left (-4-2 x-8 e^3 x+16 x^2+\left (4 x+16 e^3 x-32 x^2+\left (4 x^2+16 e^3 x^2-32 x^3\right ) \log (4)\right ) \log (x)+\left (-2 x-8 e^3 x+16 x^2+\left (-4 x-4 x^2-16 e^3 x^2+32 x^3\right ) \log (4)+\left (-2 x^3-8 e^3 x^3+16 x^4\right ) \log ^2(4)\right ) \log ^2(x)\right )}{x+\left (-2 x-2 x^2 \log (4)\right ) \log (x)+\left (x+2 x^2 \log (4)+x^3 \log ^2(4)\right ) \log ^2(x)} \, dx \]

Optimal antiderivative \[ {\mathrm e}^{2 \left ({\mathrm e}^{3}-2 x \right )^{2}-2 x +\frac {4}{1-\frac {1}{\ln \left (x \right )}+2 x \ln \left (2\right )}} \]

command

integrate(((4*(-8*x^3*exp(3)+16*x^4-2*x^3)*log(2)^2+2*(-16*x^2*exp(3)+32*x^3-4*x^2-4*x)*log(2)-8*x*exp(3)+16*x^2-2*x)*log(x)^2+(2*(16*x^2*exp(3)-32*x^3+4*x^2)*log(2)+16*x*exp(3)-32*x^2+4*x)*log(x)-8*x*exp(3)+16*x^2-2*x-4)*exp(((2*(x*exp(3)^2-4*x^2*exp(3)+4*x^3-x^2)*log(2)+exp(3)^2-4*x*exp(3)+4*x^2-x+2)*log(x)-exp(3)^2+4*x*exp(3)-4*x^2+x)/((2*x*log(2)+1)*log(x)-1))^2/((4*x^3*log(2)^2+4*x^2*log(2)+x)*log(x)^2+(-4*x^2*log(2)-2*x)*log(x)+x),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \text {Exception raised: TypeError} \]

Giac 1.7.0 via sagemath 9.3 output

\[ e^{\left (\frac {16 \, x^{3} \log \left (2\right ) \log \left (x\right )}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} - \frac {16 \, x^{2} e^{3} \log \left (2\right ) \log \left (x\right )}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} - \frac {4 \, x^{2} \log \left (2\right ) \log \left (x\right )}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} + \frac {4 \, x e^{6} \log \left (2\right ) \log \left (x\right )}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} + \frac {8 \, x^{2} \log \left (x\right )}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} - \frac {8 \, x e^{3} \log \left (x\right )}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} - \frac {8 \, x^{2}}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} + \frac {8 \, x e^{3}}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} - \frac {2 \, x \log \left (x\right )}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} + \frac {2 \, e^{6} \log \left (x\right )}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} + \frac {2 \, x}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} - \frac {2 \, e^{6}}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1} + \frac {4 \, \log \left (x\right )}{2 \, x \log \left (2\right ) \log \left (x\right ) + \log \left (x\right ) - 1}\right )} \]