MHT CET2012MathematicsIndefinite Integration
The value of e^ x [ 1+ x 1+ x ] d x is
Options
- A1 2 e^ x x 2 +C
- Be^ x x 2 +C
- C1 2 e^ x x 2 +C
- De^ x x 2 +C
Correct answer
D. e^ x x 2 +C
Step-by-step solution
Let I= e^ x [ 1+ x 1+ x ] d x aligned =& e^ x (1+ x) + e^ x x (1+ x) d x =& e^ x 2 ² x 2 d x+ e^ x 2 x 2 x 2 2 ² x 2 d x =& 1 2 e^ x ² x 2 d x+ I e^ x x 2 d x =& 1 2 e^ x ² x 2 d x + x 2 e^ x - 1 2 ² x 2 e^ x d x aligned (using integral by parts) = 1 2 e^ x ² x 2 d x+e^ x x 2 - 1 2 e^ x ² x 2 d x=e^ x x 2 +C