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MHT CET202411 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

If (7 x-2) 3 x+2 ~d x= A (3 x+2)^ 5 2 + B (3 x+2)^ 3 2 + c (where c is a constant of integration), then the values of A and B are respectively

Options

  1. A14 45 , 40 27
  2. B14 15 , -40 9
  3. C14 15 , 40 9
  4. D14 45 , -40 27

Correct answer

D. 14 45 , -40 27

Step-by-step solution

Let I = (7 x-2) 3 x+2 ~d x Let 3 x+2= t x= t -2 3 ~d x= 1 3 dt aligned & I & = [7 ( t -2 3 )-2 ] t dt & = 1 3 ( 7 t 3 - 20 3 ) t dt & = 7 9 t ^ 3 2 dt - 20 9 t ^ 1 2 dt & = 14 45 (3 x+2)^ 5 2 - 40 27 (3 x+2)^ 3 2 + C & A= 14 45 and B= -40 27 aligned

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