NDA2010MathematicsIndefinite IntegrationActual
What is x e^ x d x equal to? where c is a constant of integration.
Options
- A2 e^ x (x-2 x +2)+c
- B2 e^ x (x+2 x +2)+c
- C2 e^ x (x+2 x -2)+c
- D2 e^ x (x-2 x -2)+c
Correct answer
A. 2 e^ x (x-2 x +2)+c
Step-by-step solution
x e^ x d x Put x =u aligned & 1 2 x =d u & d x=2 x d u &= u^2 e^u d u 2 &= 2 [u^2 e^u d u- 2 u e^u d u ] &= 2 [u^2 e^u-2 e^u u-e^u ] &= 2 u^2 e^u-4 u e^u+4 e^u &= 2 x e^ x -4 x e^ x +4 e^ x &= 2 e^ x (x-2 x +2) aligned