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COMEDK2012MathematicsIndefinite Integration

If x e^ x (1+x)² d x=e^ x f(x)+c , then f(x) is equal to

Options

  1. A1 (1+x)²
  2. Bx (1+x)
  3. C1 1+x
  4. Dx (1+x)²

Correct answer

C. 1 1+x

Step-by-step solution

We have, I= x e^ x (1+x)² d x = (x+1-1) (x+1)² e^ x d x aligned &= [ 1 x+1 - 1 (x+1)² ] e^ x d x &=e^ x 1 (1+x) +C aligned On comparing, we get f(x)= 1 1+x

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