∫㏑(1+t²)dt
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![∫㏑(1+t²)dt](/uploads/image/z/11668374-54-4.jpg?t=%E2%88%AB%E3%8F%91%281%EF%BC%8Bt%26%23178%3B%29dt)
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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^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