Evaluate the indefinite integral

Question

∫ (e^u)/(1 - e^u)²  du

 

 

ANSWER: 1/(1 - e^u) + C

#17, p413

Answer 1

The indefinite integral can be evaluated from the substitution:

z = (1-e^u),

dz = -e^udu

 

∫ -1/(z²) dz

 

From power rule:

∫ -z^-2dz = z^-1 + C = (1-e^u)^-1 + C= 1/(1-e^u) + C