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MHT CET20244 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

If ( 4 e ^x-25 2 e ^x-5 ) d x= A x+ Blog (2 e ^x-5 )+ c (where c is a constant of integration) then

Options

  1. AA =5, ~B =3
  2. BA =5, ~B =-3
  3. CA =-5, ~B =3
  4. DA =-5, ~B =-3

Correct answer

B. A =5, ~B =-3

Step-by-step solution

aligned 4 e ^x-25 2 e ^x-5 ~d x & = 5 (2 e ^x-5 )-3 (2 e ^x ) 2 e ^x-5 ~d x & =5 ~d x-3 2 e ^x 2 e ^x-5 ~d x & =5 x-3 |2 e ^x-5 |+ c A =5 and B & =-3 aligned

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