BITSAT2021MathematicsIndefinite IntegrationActual
e^ x (1+x) ² (e^ x x ) dx equals
Options
- A- (e x^ x )+ C
- B(x e^ x )+ C
- C(e^ x )+ C
- D(e^ x )+ C
Correct answer
B. (x e^ x )+ C
Step-by-step solution
e^ x (1+x) ² (e^ x x ) dx Let x e^ x =t (x e^ x +e^ x )= dt dx d x= dt e^ x (x+1) e^ x (1+x) ² (e^ x x ) dx = e^ x (1+x) ² t d t e^ x (1+x) = 1 ² t dt = ² t dt = t+ C = (x e^ x )+ C