简单计算一下即可，答案如图所示
求下列不定积分 ∫(arctan e^x)\/(e^2x)dx
d(1\/e^x)=-1\/e^x
求解arctan e^x\/e^(2x)的不定积分
简单计算一下即可，答案如图所示
求过程 不定积分 arctane^x\/e^x
解：分部积分 ∫(arctane^x)\/e^xdx =∫e^(-x)·(arctane^x) dx =-e^(-x)·(arctane^x)+∫e^(-x)·1\/(1+e^(2x))·e^x dx =-e^(-x)·(arctane^x)+∫1\/(1+e^(2x)) dx =-e^(-x)·(arctane^x)+∫e^(-2x)\/[e^(-2x)+1] dx =-e^(-x)·(arctane...
求不定积分∫arctane^x\/e^(2x) dx
简单计算一下即可，答案如图所示
求不定积分∫arctane^x\/e^(2x) dx?
令y=arctane^x,则e^x=tany,x=ln(tany)dx=cotysec^2ydy 原式=∫ycot^2y*cotysec^2ydy =∫ycsc^2ycotydy =∫ycosy\/sin^3ydy =∫y\/sin^3ydsiny =(-1\/2)∫yd(1\/sin^2y)=(-1\/2)y\/sin^2y+1\/2∫dy\/sin^2y =(-1\/2)ycsc^2y-1\/2coty+C =(-1\/2)arctane^xcsc^2(arc...
求不定积分∫arctane^x\/e^(2x) dx
令y=arctane^x,则e^x=tany,x=ln(tany)dx=cotysec^2ydy 原式=∫ycot^2y*cotysec^2ydy =∫ycsc^2ycotydy =∫ycosy\/sin^3ydy =∫y\/sin^3ydsiny =(-1\/2)∫yd(1\/sin^2y)=(-1\/2)y\/sin^2y+1\/2∫dy\/sin^2y =(-1\/2)ycsc^2y-1\/2coty+C =(-1\/2)arctane^xcsc^2(arc...
求解arctan e^x\/e^(2x)的不定积分
=-arctan(e^x) \/ e^x + ∫ dx\/(1+e^(2x) )let e^x= tany e^x dx = (secy)^2 dy ∫ dx\/(1+e^(2x) )= ∫ [1\/(secy)^2] . [(secy)^2\/tany] dy = ∫ (cosy\/siny) dy = ln|siny|+C'= ln| e^x\/√(1+e^2x) | + C'∫(arctan e^x)\/(e^x) ...
计算不定积分∫arctane∧x\/e∧2xdx?
回答：能否把原始题目拍个照,这个题目不确定
求解不定积分题目
简单计算一下，答案如图所示
