Integration By Parts

The correct answer is D:

%5Cfrac%7B1%7D%7B2%7D%5Cfrac%7Be%5E%7Bx%5E%7B2%7D%7D%7D%7B(3%2Bx%5E2)%7D%2Bk

Put

x%5E%7B2%7D%3Dt%20%5CRightarrow%202%20x%20d%20x%3Dd%20t

I%3D%5Cint%20%5Cfrac%7Be%5E%7Bx%5E%7B2%7D%7D%5Cleft(2%2Bx%5E%7B2%7D%5Cright)%20x%20d%20x%7D%7B%5Cleft(3%2Bx%5E%7B2%7D%5Cright)%5E%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%5Cint%20e%5E%7Bt%7D%20%5Cfrac%7B(2%2Bt)%7D%7B(3%2Bt)%5E%7B2%7D%7D%20d%20t

%3D%5Cfrac%7B1%7D%7B2%7D%20%5Cint%20%5Cfrac%7Be%5E%7Bt%7D(3%2Bt-1)%7D%7B(3%2Bt)%5E%7B2%7D%7D%20d%20t%3D%5Cfrac%7B1%7D%7B2%7D%20%5Cint%20e%5E%7Bt%7D%5Cleft%5B%5Cfrac%7B1%7D%7B3%2Bt%7D-%5Cfrac%7B1%7D%7B(3%2Bt)%5E%7B2%7D%7D%5Cright%5D%20d%20t

%3D%5Cfrac%7B1%7D%7B2%7D%20e%5E%7Bt%7D%20%5Cfrac%7B1%7D%7B3%2Bt%7D%2Bk%5Cleft%5B%5Cbecause%20%5Cfrac%7Bd%7D%7Bd%20t%7D%5Cleft(%5Cfrac%7B1%7D%7B3%2Bt%7D%5Cright)%3D%5Cfrac%7B-1%7D%7B(3%2Bt)%5E%7B2%7D%7D%5Cright%5D

%3D%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7Be%5E%7Bx%5E%7B2%7D%7D%7D%7B3%2Bx%5E%7B2%7D%7D%2Bk

Chapter Questions
1 MCQs