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BITSAT2022MathematicsIndefinite IntegrationActual

The value of 1 [(x-1)^3(x+2)^5 ]^ 1 4 d x , is

Options

  1. A4 3 ( x+1 x-2 )^ 1 4 +C
  2. B3 4 ( x-1 x+2 )^ 1 4 +C
  3. C4 3 ( x-1 x+2 )^ 1 4 +C
  4. D1 3 ( 2 x-1 4 x-3 )^ 1 4 +C

Correct answer

C. 4 3 ( x-1 x+2 )^ 1 4 +C

Step-by-step solution

I= 1 ( x-1 x+2 )^ 3 / 4 (x+2)^2 d x Let x-1 x+2 =t 3 d x (x+2)^2 =d t aligned I & = 1 3 1 t^ 3 / 4 d t= 1 3 ( t^ 1 / 4 1 / 4 )+C & = 4 3 t^ 1 / 4 +C= 4 3 ( x-1 x+2 )^ 1 / 4 +C aligned

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