KCET2024MathematicsIndefinite Integration
1 x [6( x)^2+7 x+2 ] d x is
Options
- A1 2 | 2 x+1 3 x+2 |+C
- B| 2 x+1 3 x+2 |+C
- C| 3 x+2 2 x+1 |+C
- D1 2 | 3 x+2 2 x+1 |+C
Correct answer
B. | 2 x+1 3 x+2 |+C
Step-by-step solution
I= 1 x [6( x)^2+7 x+2 ] d x= d t 6 t^2+7 t+2 [ array l put t= x d t= 1 x d x array ]= d t (3 t+2)(2 t+1) Now, 1 (3 t+2)(2 t+1) = A (3 t+2) + B (2 t+1) = A(2 t+1)+B(3 t+2) (3 t+2)(2 t+1) 1=A(2 t+1)+B(3 t+2) Now, on putting t= -1 2 1=0+B [3 (- 1 2 )+2 ] B=2 and put t= -2 3 1=A (2 (- 2 3 )+1 )+0 1=A (- 4 3 +1 ) A=-3 I= ( -3 3 t+2 + 2 2 t+1 ) d t= -3 |3 t+2| 3 +2 |2 t+1| 2 +C=- |3 t+2|+ |2 t+1|+C= | 2 t+1 3 t+2 |+C= | 2 x+1 3 x+2 |+C [ t= x]