22.48 Problem number 8818

$$\int \frac{-2+x+((-12+7x)\log (3)+(12-7x)\log (x))\log (-\log (3)+\log (x))}{(-256x^7+256x^8-64x^9)\log (3)+(256x^7-256x^8+64x^9)\log (x)}dx$$

Optimal antiderivative $$\frac{\ln (\ln \left(x\right)-\ln \left(3\right))}{64x^6(-2+x)}$$

command

Integrate[(-2 + x + ((-12 + 7*x)*Log[3] + (12 - 7*x)*Log[x])*Log[-Log[3] + Log[x]])/((-256*x^7 + 256*x^8 - 64*x^9)*Log[3] + (256*x^7 - 256*x^8 + 64*x^9)*Log[x]),x]

Mathematica 13.1 output

$$\int \frac{-2+x+((-12+7x)\log (3)+(12-7x)\log (x))\log (-\log (3)+\log (x))}{(-256x^7+256x^8-64x^9)\log (3)+(256x^7-256x^8+64x^9)\log (x)}dx$$

Mathematica 12.3 output

$$\frac{\log (\log \left(\frac{x}{3}\right))}{64(-2+x)x^6}$$