COMEDK2013MathematicsIndefinite Integration
x e^ x d x is equal to
Options
- A2 x -e^ x -4 x e^ x +c
- B(2 x-4 x +4) e^ x +c
- C(2 x+4 x +4) e^ x +c
- D(1-4 x ) e^ x +c
Correct answer
B. (2 x-4 x +4) e^ x +c
Step-by-step solution
Let I= x e^ x d x Put x =t x=t² d x=2 t d t aligned I &=2 t² e^ t d t &=2 [t² e^ t - e^ t 2 t d t ] &=2 [t² e^ t -2 t e^ t d t ] &=2 [t² e^ t -2 (t e^ t - e^ t 1 d t ) ] &=2 [t² e^ t -2 t e^ t +2 e^ t ]+c &= (2 t²-4 t+4 ) e^ t +c &=(2 x-4 x +4) e^ x +c aligned