43.67 Problem number 10096

$$\int \frac{8000+4800x+960x^2-56x^3-12x^4+(6000+2400x+240x^2-35x^3)\log (x)+(1500+300x){\log }^2(x)+125{\log }^3(x)}{(8000x+4800x^2+960x^3+44x^4-4x^5+(6000x+2400x^2+240x^3-5x^4)\log (x)+(1500x+300x^2){\log }^2(x)+125x{\log }^3(x))\log \left(\frac{160000x+128000x^2+38400x^3+4320x^4-64x^5-32x^6+x^7+(160000x+96000x^2+19200x^3+880x^4-80x^5)\log (x)+(60000x+24000x^2+2400x^3-50x^4){\log }^2(x)+(10000x+2000x^2){\log }^3(x)+625x{\log }^4(x)}{160000+128000x+38400x^2+5120x^3+256x^4+(160000+96000x+19200x^2+1280x^3)\log (x)+(60000+24000x+2400x^2){\log }^2(x)+(10000+2000x){\log }^3(x)+625{\log }^4(x)}\right)}dx$$

Optimal antiderivative $$\ln \left(\ln \left(\frac{{(x-\frac{x^4}{{(4x+20+5\ln \left(x\right))}^2})}^2}{x}\right)\right)$$

command

integrate((125*log(x)^3+(300*x+1500)*log(x)^2+(-35*x^3+240*x^2+2400*x+6000)*log(x)-12*x^4-56*x^3+960*x^2+4800*x+8000)/(125*x*log(x)^3+(300*x^2+1500*x)*log(x)^2+(-5*x^4+240*x^3+2400*x^2+6000*x)*log(x)-4*x^5+44*x^4+960*x^3+4800*x^2+8000*x)/log((625*x*log(x)^4+(2000*x^2+10000*x)*log(x)^3+(-50*x^4+2400*x^3+24000*x^2+60000*x)*log(x)^2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+160000*x)*log(x)+x^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000*x)/(625*log(x)^4+(2000*x+10000)*log(x)^3+(2400*x^2+24000*x+60000)*log(x)^2+(1280*x^3+19200*x^2+96000*x+160000)*log(x)+256*x^4+5120*x^3+38400*x^2+128000*x+160000)),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

$$\log (-\log (x^6-32x^5-80x^4\log \left(x\right)-50x^3\log {\left(x\right)}^2-64x^4+880x^3\log \left(x\right)+2400x^2\log {\left(x\right)}^2+2000x\log {\left(x\right)}^3+625\log {\left(x\right)}^4+4320x^3+19200x^2\log \left(x\right)+24000x\log {\left(x\right)}^2+10000\log {\left(x\right)}^3+38400x^2+96000x\log \left(x\right)+60000\log {\left(x\right)}^2+128000x+160000\log \left(x\right)+160000)+\log (256x^4+1280x^3\log \left(x\right)+2400x^2\log {\left(x\right)}^2+2000x\log {\left(x\right)}^3+625\log {\left(x\right)}^4+5120x^3+19200x^2\log \left(x\right)+24000x\log {\left(x\right)}^2+10000\log {\left(x\right)}^3+38400x^2+96000x\log \left(x\right)+60000\log {\left(x\right)}^2+128000x+160000\log \left(x\right)+160000)-\log \left(x\right))$$