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NDA2022MathematicsIndefinite IntegrationActual

What is ( x)^ -1 / 2 ( x)^ -3 / 2 d x equal to?

Options

  1. Ax +c
  2. B2 x +c
  3. Cx +c
  4. D2 x +c

Correct answer

B. 2 x +c

Step-by-step solution

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

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