22.20 Problem number 3121

$$\int \frac{3^{-1/x}\sqrt[x]{\log \left(x^4\right)}(-48+12\log \left(x^4\right)\log \left(\frac{\log \left(x^4\right)}{3}\right))}{(625x^2+50x^2\log (4)+x^2{\log }^2(4))\log \left(x^4\right)+3^{-1/x}(-50x^2-2x^2\log (4)){\log }^{1+\frac{1}{x}}\left(x^4\right)+3^{-2/x}{x}^2{\log }^{1+\frac{2}{x}}\left(x^4\right)}dx$$

Optimal antiderivative $$\frac{12}{-25-2\ln \left(2\right)+{\mathrm{e}}^{\frac{\ln \left(\frac{\ln \left(x^4\right)}{3}\right)}{x}}}$$

command

Integrate[(Log[x^4]^x^(-1)*(-48 + 12*Log[x^4]*Log[Log[x^4]/3]))/(3^x^(-1)*((625*x^2 + 50*x^2*Log[4] + x^2*Log[4]^2)*Log[x^4] + ((-50*x^2 - 2*x^2*Log[4])*Log[x^4]^(1 + x^(-1)))/3^x^(-1) + (x^2*Log[x^4]^(1 + 2/x))/3^(2/x))),x]

Mathematica 13.1 output

$$\int \frac{3^{-1/x}\sqrt[x]{\log \left(x^4\right)}(-48+12\log \left(x^4\right)\log \left(\frac{\log \left(x^4\right)}{3}\right))}{(625x^2+50x^2\log (4)+x^2{\log }^2(4))\log \left(x^4\right)+3^{-1/x}(-50x^2-2x^2\log (4)){\log }^{1+\frac{1}{x}}\left(x^4\right)+3^{-2/x}{x}^2{\log }^{1+\frac{2}{x}}\left(x^4\right)}dx$$

Mathematica 12.3 output

$$-\frac{43^{1+\frac{1}{x}}}{3^{\frac{1}{x}}(25+\log (4))-\sqrt[x]{\log \left(x^4\right)}}$$