KCET2021MathematicsIndefinite Integration
The value of e^ x [ 1+ x 1+ x ] d x is equal to
Options
- Ae^ x x 2 +C
- Be^ x x+C
- Ce^ x (1+ x)+C
- De^ x (1+ x)+C
Correct answer
A. e^ x x 2 +C
Step-by-step solution
Let 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 [ ² x 2 2 + x 2 ] d x Let f(x)= x 2 f^ (x)= ² x 2 2 Using the formula, e^ x [f(x)+f^ (x) ] d x aligned &=e^ x f(x)+C I &=e^ x x 2 +C aligned