KCET2020MathematicsIndefinite Integration
The value of e^ x 2 x d x is
Options
- A2 e^ x ( x-1)+C
- B2 e^ x ( x+1)+C
- C2 e^ x ( x+1)+C
- D2 e^ x ( x-1)+C
Correct answer
A. 2 e^ x ( x-1)+C
Step-by-step solution
We have, e^ x 2 x d x aligned &= e^ x (2 x x) d x &=2 e^ x x x d x aligned let x=t aligned x d x &=d t=2 e^ t t d t &=2 [t e^ t d t- ( d d t (t) e^ t d t ) d t ] &=2 [t e^ t - e^ t d t ] &=2 [t e^ t -e^ t ]+C &=2 [e^ t (t-1) ]+C &=2 [e^ x ( x-1) ]+C &=2 e^ x ( x-1)+C aligned