60270560   
   From: Albert_Rich@msn.com   
      
   On Friday, April 28, 2017 at 5:50:01 AM UTC-10, Andreas Dieckmann wrote:   
   > The shortest form I could find is   
   > Integrate[(Log[a + b*x]*Log[c + d*x])/(e + f*x), x] =   
   > (1/f)*(Log[a + b*x]*Log[c + d*x]*Log[(b*(e + f*x))/(b*e - a*f)] -   
   >          (1/2)*Log[(b*(c*f - d*e))/(d*(a*f - b*e))]*   
   >      Log[((a*f - b*e)*(a + b*x))/f]*Log[(f*(a + b*x))/(a*f - b*e)] +   
   >     Log[c + d*x]*PolyLog[2, (f*(a + b*x))/(a*f - b*e)] +   
   >          Log[a + b*x]*PolyLog[2, (f*(c + d*x))/(c*f - d*e)] -   
   >     Log[((a*f - b*e)*(c + d*x))/((c*f - d*e)*(a +   
   >            b*x))]*(Log[(b*(c*f - d*e))/(d*(a*f - b*e))]*Log[a + b*x] -   
   >               PolyLog[2, (f*(c + d*x))/(c*f - d*e)] +   
   >        PolyLog[2, (f*(a + b*x))/(a*f - b*e)] -   
   >        PolyLog[2, (b*(c + d*x))/(d*(a + b*x))] +   
   >                PolyLog[2, ((a*f - b*e)*(c + d*x))/((c*f - d*e)*(a + b*x))]) -   
   >     PolyLog[3, (f*(a + b*x))/(a*f - b*e)] -   
   >     PolyLog[3, (f*(c + d*x))/(c*f - d*e)] -   
   >          PolyLog[3, (b*(c + d*x))/(d*(a + b*x))] +   
   >     PolyLog[3, ((a*f - b*e)*(c + d*x))/((c*f - d*e)*(a + b*x))])   
   >   
   > Andreas   
      
   What Rubi needs to know is how to derive it.   
      
   Albert   
      
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