If 2 e^x+3 e^ -x 3 e^x+4 e^ -x d x=A x+B (3 e^ 2 x +4 )+C , then values of A and B are respectively (where C is a constant of integration.)

Step-by-step solution

aligned & 2 e^x+3 e^ -x 3 e^x+4 e^ -x d x= 2 e^ 2 x +3 3 e^ 2 x +4 d x & 3 4 (3 e^ 2 x +4 )- 1 24 (6 e^ 2 x ) 3 e^ 2 x +4 d x & = 3 4 x- 1 24 (3 e^ 2 x +4 )+c & A= 3 4 and B= -1 24 aligned