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MHT CET20249 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

x^4+x^2+1 x^2-x+1 ~d x is equal to

Options

  1. Ax^3 3 - x^2 2 +x+ c , (where c is a constant of integration)
  2. Bx^3 3 + x^2 2 +x+ c , (where c is a constant of integration)
  3. Cx^3 3 - x^2 2 -x+ c , (where c is a constant of integration)
  4. Dx^3 3 + x^2 2 -x+ c , ( where c is a constant of integration)

Correct answer

B. x^3 3 + x^2 2 +x+ c , (where c is a constant of integration)

Step-by-step solution

aligned I & = x^4+x^2+1 x^2-x+1 & = ( x^2-x+1+x^4+x x^2-x+1 ) d x & = x^2-x+1 x^2-x+1 ~d x+ (x^4+x ) x^2-x+1 ~d x & = 1 ~d x+ x (x^3+1 ) x^2-x+1 ~d x & =x+ x(x+1) (x^2-x+1 ) (x^2-x+1 ) d x & =x+ (x^2+x ) d x=x+ x^3 3 + x^2 2 + c aligned

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