Question

求不定积分arctane^x/e^xdx

Answer 1

简单计算一下即可，答案如图所示

Answer 2

I = ∫ arctan(e^x) d(-e^(-x)) = - e^(-x) * arctan(e^x) + ∫ 1/(1+e^(2x)) dx= - e^(-x) * arctan(e^x) + ∫ e^(-2x) /(e^(-2x)+1) dx = - e^(-x) * arctan(e^x) + (-1/2) ln[ e^(-2x) + 1] + C