∫上1下0 e^x(1+e^x)^3dx
=∫上1下0 (1+e^x)^3d(e^x)
=∫上1下0 (1+e^x)^3d(1+e^x)
=(1/4)(1+e^x)^4|<0,1>
=(1/4)[(1+e^1)^4-(1+e^0)^4]
=(1/4)[(1+e)^4-2^4]
=[(1+e)^4-16]/4