15.

 

A. ln (1 + e-1)

B. - ln (1 + e-1)

C. ln (1 + e)

D. arctan (e1/2)

E. does not exist

 

 

 

Solution: The answer is A

 

The given integral, 

 

is an improper integral whose value is given by, 

Letting, 

 

Thus, taking the limit as b goes to infinity yields,