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AP EAMCET2004MathematicsIndefinite Integration

3-x^2 1-2 x+x^2 e^x d x=e^x f(x)+c f(x)

Options

  1. A1+x 1-x
  2. B1-x 1+x
  3. C1+x x-1
  4. Dx-1 1+x

Correct answer

A. 1+x 1-x

Step-by-step solution

Let aligned I & = 3-x^2 1-2 x+x^2 e^x d x & = 3-x^2 (1-x)^2 e^x d x & = ( 2 (1-x)^2 + 1+x 1-x ) e^x d x aligned From Eqs. (i) and (ii), we get aligned & e^x ( 1+x 1-x )+c=e^x f(x)+c & f(x)= 1+x 1-x & aligned

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