Indefinite Integration (20點!!)

∫ 2x / ((x^2)+1)ln((x^2)+1) dx

Notice that [ln(x^2+1)]'=2x/(x^2+1). The original integration becomes

∫ 2x / ((x^2)+1)ln((x^2)+1) dx
=∫ 1 / ln((x^2)+1) d [ln(x^2+1)]
=ln[ln(x^2+1)] + C where C is a constant

HOPE IT HELPS