43.19 Problem number 2446

\[ \int \frac {e^{\frac {1}{3} \left (-e^{-4+\sqrt [4]{x}}-3 x \log (3)\right )} \left (-e^{-4+\sqrt [4]{x}} \sqrt [4]{x}-12 x \log (3)\right )}{48 x} \, dx \]

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

command

integrate(1/48*(-x^(1/4)*exp(x^(1/4)-4)-12*x*log(3))*exp(-1/3*exp(x^(1/4)-4)-x*log(3))/x,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

\[ \frac {1}{4} \, e^{\left (-{\left (x^{\frac {1}{4}} - 4\right )}^{4} \log \left (3\right ) - 16 \, {\left (x^{\frac {1}{4}} - 4\right )}^{3} \log \left (3\right ) - 96 \, {\left (x^{\frac {1}{4}} - 4\right )}^{2} \log \left (3\right ) - 256 \, {\left (x^{\frac {1}{4}} - 4\right )} \log \left (3\right ) - \frac {1}{3} \, e^{\left (x^{\frac {1}{4}} - 4\right )} - 256 \, \log \left (3\right )\right )} \]