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KCET2021MathematicsIndefinite Integration

The value of x e^ x d x (1+x)² is equal to

Options

  1. Ae^ x (1+x)+C
  2. Be^ x (1+x² )+C
  3. Ce^ x (1+x)²+C
  4. De^ x 1+x +C

Correct answer

D. e^ x 1+x +C

Step-by-step solution

Let I= x e^ x d x (1+x)² = e^ x (x+1-1) (1+x)² d x= e^ x [ 1 1+x + ( -1 (1+x)² ) ] d x Let 1 1+x =f(x) f^ (x)=- 1 (1+x)² Using the formula, e^ x [f(x)+f^ (x) ] d x=e^ x f(x)+C I=e^ x ( 1 1+x )+C= e^ x 1+x +C

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