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MHT CET20243 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

The value of e ^x ( 1- x 1- x ) dx is equal to

Options

  1. A- e ^x x 2 + c , (where c is a constant of integration)
  2. Be ^x x 2 + c , (where c is a constant of integration)
  3. Ce ^x cosec x 2 + c , ( where c is a constant of integration)
  4. D- e ^x cosec x 2 + c , (where c is a constant of integration)

Correct answer

A. - e ^x x 2 + c , (where c is a constant of integration)

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

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