∫㏑(1＋t²)dt
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∫㏑(1＋t²)dt∫㏑(1＋t²)dt∫㏑(1＋t²)dt∫㏑(1＋t^2)dt=tln(1+t^2)-2∫t^2/(1＋t^2)dt=tln(1+t^2)-2∫(t^
∫㏑(1＋t²)dt
∫㏑(1＋t²)dt
∫㏑(1＋t²)dt
∫㏑(1＋t^2)dt
=tln(1+t^2) - 2∫t^2/(1＋t^2)dt
=tln(1+t^2) - 2∫(t^2+1)/(1＋t^2)dt +2∫dt/(1＋t^2)
=tln(1+t^2) - 2t +2arctan(t) + C
原式
=tln(1+t^2)-∫td(ln(1+t^2))
=tln(1+t^2)-∫2t^2/(1+t^2)dt
=tln(1+t^2)-2∫1dt+2∫1/(1+t^2)dt
=tln(1+t^2)-2t+2arctant+c