∫(arctan e^x)/(e^x) dx ,e^x 是e的x次幂.

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∫(arctane^x)/(e^x)dx,e^x是e的x次幂.∫(arctane^x)/(e^x)dx,e^x是e的x次幂.∫(arctane^x)/(e^x)dx,e^x是e的x次幂.令e^x=t则

∫(arctan e^x)/(e^x) dx ,e^x 是e的x次幂.
∫(arctan e^x)/(e^x) dx ,e^x 是e的x次幂.

∫(arctan e^x)/(e^x) dx ,e^x 是e的x次幂.
令e^x=t
则原式=∫arctant/t*1/tdt
=∫arctant/t^2dt
=-∫arctantd(1/t)
=-arctant/t+∫1/t*1/(t^2+1)dt
=-arctant/t+∫(1/t-t/(t^2+1))dt
=-arctant/t+∫dt/t-1/2∫d(t^2+1)/(t^2+1)
=-arctant/t+ln|t|-1/2ln|t^2+1|+C
=-arctan(e^x)/e^x+x-1/2ln(e^(2x)+1)+C