AP EAMCET2008MathematicsIndefinite Integration
If e^x(1+x) ^2 (x e^x ) d x=f(x)+ constant, then f(x) is equal to
Options
- A(x e^x .
- B(x e^x .
- C2 ⁻¹(x)
- D(x e^x )
Correct answer
D. (x e^x )
Step-by-step solution
Given that, e^x(1+x) ^2 (x e^x ) d x=f(x)+ constant Put x e^x=t in LHS aligned & & (e^x+x e^x ) d x & =d t & & LHS & = ^2 t d t & & & = t+ constant & & (x e^x )+ constant & =f(x)+ constant & & f(x) & = (x e^x ) aligned