∫xIIlog(1+x2)Idx
=log(1+x2)∫x⋅dx−∫[log(1+x2)]′∫xdx⋅dx
=x22⋅log(1+x2)−∫2x1+x2×x22⋅dx
=x22⋅log(1+x2)−∫x31+x2I1⋅dx I1:1+x2)x3(x
=x22⋅log(1+x2)−∫x31+x2⋅dx x3+x
=x22⋅log(1+x2)−x22+12∫2x1+x2⋅dx _________
Let (1+x2)=t −x
2x⋅dx=dt
=x22⋅log(1+x2)−x22+12∫dtt
=x22log(1+x2)−x22+12logt+c
=x22log(1+x2)−x22+12log|1+x2|+c.
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