MHT CET2012MathematicsIndefinite Integration
The value of 1 3 x- x+3 d x is
Options
- A( x 2 +1 2 x 2 +1 )+C
- B1 2 ( 2 x 2 +1 x 2 +1 )+C
- C( 2 x 2 +1 x 2 +1 )+C
- D2 ( 2 x 2 +1 x 2 +1 )+C
Correct answer
C. ( 2 x 2 +1 x 2 +1 )+C
Step-by-step solution
Let I= d x 3 x- x+3 array l x= 2 x 2 1+ ² x 2 and x= 1- ² x 2 1+ ² x 2 array I= d x 3 2 x 2 1+ ² x 2 - 1- ² x 2 1+ ² x 2 +3 = (1+ ² x 2 ) d x 6 x 2 -1+ ² x 2 +3+3 ² x 2 = ² x 2 4 ² x 2 +6 x 2 +2 d x ( . let .t= x 2 , d t= 1 2 ² x 2 d x )= d t 2 t²+3 t+1 = d t (t+1)(2 t+1) = -1 (t+1) + 2 (2 t+1) d t (by partial fraction) =- (t+1)+ 2 2 (2 t+1)+C= (2 t+1) (t+1) +C= ( 2 x 2 +1 x 2 +1 )+C