令t=e^x.则x=lnt
∫(arctan(e^x)/e^(2x))dx
=∫(arctant/t²)dlnt
=∫(arctant/t³)dt
= -1/2∫arctantd(1/t²)
=-1/2(arctant/t²-∫(1/t²)darctant)
=-1/2(arctant/t²-∫(1/(t²(t²+1))dt)
=-1/2(arctant/t²-∫((1/t²)-(1/(t²+1))dt)
=-1/2(arctant/t²-∫(1/t²)dt+∫(1/(t²+1))dt
=-1/2(arctant)/t²-1/(2t)-(arctant/)2+C
=-1/2(arctane^x)/e^(2x)-1/(2e^x)-(arctane^x)/2+C
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