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AP EAMCET20225 Jul 2022Morning ShiftMathematicsIndefinite IntegrationActual

d x (x-3)^ 4 5 (x+1)^ 6 5 =

Options

  1. A5 4 [5] x-3 x+1 +C
  2. B5 4 ( x+1 x-3 )^ 1 5 +C
  3. C1 5 ( x-3 x+1 )^ 1 5 +C
  4. D5 4 ( x-3 x+4 )^ 4 5 +C

Correct answer

A. 5 4 [5] x-3 x+1 +C

Step-by-step solution

Let I= d x (x+1)^ 6 5 (x-3)^ 4 5 I= d x (x+1)^2 ( x-3 x+1 )^ 4 5 On putting (x-3) (x+1) =t , then d t= 4 (x+1)^2 d xI= d t 4 t^ 4 5 = 5 4 t^ 1 5 +C= 5 4 ( x-3 x+1 )^ 1 5 +C

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