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MHT CET202313 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

(x^2+ a ^2 ) x^2 ~d x=

Options

  1. A- (x^2+ a ^2 ) x + 1 a ⁻¹ x a + c , where c is a constant of integration.
  2. B- (x^2+ a ^2 ) x + 2 a ⁻¹ x a + c , where c is a constant of integration.
  3. C(x^2+ a ^2 ) x^2 - 1 a ⁻¹ x a + c , where c is a constant of integration.
  4. D(x^2+ a ^2 ) x^2 - 2 a ⁻¹ x a + c , where c is a constant of integration.

Correct answer

B. - (x^2+ a ^2 ) x + 2 a ⁻¹ x a + c , where c is a constant of integration.

Step-by-step solution

Let aligned I & = (x^2+ a ^2 ) x^2 ~d x & = (x^2+ a ^2 ) x⁻² ~d x & = (x^2+ a ^2 ) x⁻² ~d x & - d d x [ (x^2+ a ^2 ) ] x⁻² ~d x d x & = (x^2+ a ^2 ) (- 1 x )- 2 x x^2+ a ^2 (- 1 x ) d x & =- (x^2+ a ^2 ) x +2 1 x^2+ a ^2 ~d x & =- (x^2+ a ^2 ) x + 2 a ⁻¹ ( x a )+ c aligned

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