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AP EAMCET202422 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

x^3 ⁻¹ x^4 1+x^8 d x=

Options

  1. A( ⁻¹ (x^4 ) )^2 8 +c
  2. B( ⁻¹ (x^4 ) )^3 3 +c
  3. C( ⁻¹ (x^4 ) )^2 4 +c
  4. D( ⁻¹ (x^4 ) )^2 2 +c

Correct answer

A. ( ⁻¹ (x^4 ) )^2 8 +c

Step-by-step solution

aligned & Let I= x^3 ⁻¹ x^4 1+x^8 d x & Let x^4=t x^3 d x= 1 4 d t & I= 1 4 ⁻¹ t 1+t^2 d t, Let ⁻¹ t=d u & 1 1+t^2 d t=d u & I= 1 4 t d t I= 1 8 t^2+c & I= 1 8 ( ⁻¹ (x^4 ) )^2+c . aligned

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