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AP EAMCET202419 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

( x x x- x )^2 d x=

Options

  1. Ax cosec x x x- x + x+c
  2. Bx cosec x x x- x - x+c
  3. Cx cosec x x x+ x + x+c
  4. Dx x x- x - x+c

Correct answer

B. x cosec x x x- x - x+c

Step-by-step solution

Let I= ( x x x- x )^2 d x aligned & = x^2 (x x- x)^2 d x & =- x x (-x x) (x x- x)^2 d x & = -x x (-1) (x x- x) - x-x x ^2 x(x x- x) d x & = x x(x x- x) + cosec ^2 x d x & = x cosec x x x- x - x+c . aligned

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