KCET2015MathematicsDifferentiation
( e^ x ( 1+ x 1+ x ) d x ) is
Options
- A( e^ x ( x 2 )+C )
- B( ( x 2 )+C )
- C( e^ x +C )
- D( e^ x x+C )
Correct answer
A. ( e^ x ( x 2 )+C )
Step-by-step solution
Given that, ( I= e^ x ( 1+ x 1+ x ) d x ) ( = e^ x ( 1+2 ( x 2 ) ( x 2 ) 2 ² ( x 2 ) ) d x ) ( = e^ x [ 1 2 ² ( x 2 ) + ( x 2 ) ² ( x 2 ) ] d x ) ( = e^ x ( 1 2 ² ( x 2 )+ ( x 2 ) ) d x ) Let ( u= ( x 2 ) then d u d x = 1 2 ² x 2 ) So, ( I= e^ x [u+ d u d x ] d x=e^ x u ) ( =e^ x ( x 2 )+c )