∫xex/(1+x)2dx
∫[xex/(1+x2)]dx=∫[(ex+xex-ex)/(1+x)2]dx = ∫[ex/(1+x)]-∫[ec(1+x2)]dx =∫[1/(1+x)dex+∫exd1/(1+x) =ex/(1+x)-∫exd1/(1+x)+∫exd 1/(1+x)=ex/(1+x)+C
∫xex/(1+x)2dx
∫[xex/(1+x2)]dx=∫[(ex+xex-ex)/(1+x)2]dx = ∫[ex/(1+x)]-∫[ec(1+x2)]dx =∫[1/(1+x)dex+∫exd1/(1+x) =ex/(1+x)-∫exd1/(1+x)+∫exd 1/(1+x)=ex/(1+x)+C