4 e^ x +6 e^ -x 9 e^ x -4 e^ -x d x=A x+B |9 e^ 2 x -4 |+c , then (Where c is constant of integration)

Step-by-step solution

I= 4 e^ 2 x +6 9 e^ 2 x -4 d x4 e^ 2 x +6=A (18 e^ 2 x )+B (9 e^ 2 x -4 )...(1)4 e^ 2 x +6=(18 A+9 B) e^ 2 x -4 B -4 ~B =6 B = -3 2 and 18 ~A +9 ~B =4 18 ~A - 9 3 2 =4 18 ~A = 35 2 A = 35 36 4 e^ 2 x +6= 35 36 (18 e^ 2 x )- 3 2 (9 e^ 2 x -4 )I= [ 35 36 (18 e^ 2 x ) 9 e^ 2 x -4 - 3 2 (9 e^ x -4 ) 9 e^ x -4 ] d xI= 35 36 |9 e^ 2 x -4 |- 3 2 x+c=A x+B |9 e^ 2 x -4 |+c A =- 3 2 and B = 35 36