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(Log[b + a*x]*Log[(a*(d + c*x))/(-(b*c) + a*d)] + PolyLog[2, (c*(b + a*x))/(b*c - a*d)])/c


Integrate[Log[b + a*x]/(d + c*x), x] ==
(Log[b + a*x]*Log[(a*(d + c*x))/(-(b*c) + a*d)] + PolyLog[2, (c*(b + a*x))/(b*c - a*d)])/c



          Log[b + a x]
Integrate[------------, x] == 
            d + c x

                  a (d + c x)
(Log[b + a x] Log[------------] + 
                  -(b c) + a d
 
               c (b + a x)
    PolyLog[2, -----------]) / c
                b c - a d

Time to compute: 0.03 second

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