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AP EAMCET2008MathematicsIndefinite Integration

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

Options

  1. Ae^x ( x 2 )+c
  2. Be^ -x ( x 2 )+c
  3. C-e^x ( x 2 )+c
  4. D-e^ -x ( x 2 )+c

Correct answer

C. -e^x ( x 2 )+c

Step-by-step solution

aligned & e^x ( 1- x 1- x ) d x & = e^x ( 1-2 x 2 x 2 2 ^2 x 2 ) d x & = 1 2 e^x ( cosec ^2 x 2 ) d x- e^x x 2 d x & = 1 2 [-e^x x 2 2+ e^x x 2 2 d x ] & =-e^x x 2 +c aligned

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