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MHT CET202310 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

e ^x (1- x+ ^2 x ) d x=

Options

  1. Ae ^x x+ c , where c is a constant of integration.
  2. Be ^x cosec x+ c , where c is a constant of integration.
  3. C- e ^x x+ c , where c is a constant of integration.
  4. D- e ^x cosec x+ c , where c is a constant of integration.

Correct answer

C. - e ^x x+ c , where c is a constant of integration.

Step-by-step solution

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

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