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AP EAMCET202316 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

x^4+x⁻⁴+2 x^3 d x=

Options

  1. A|x|- 1 4 x^4 +C
  2. B|x|+ 1 4 x^4 +C
  3. C|x|- 4 x^4 +C
  4. D|x|+ 4 x^4 +C

Correct answer

A. |x|- 1 4 x^4 +C

Step-by-step solution

Let I= x^4+x⁻⁴+2 x^3 d x aligned & I= (x^2 )^2+ (x⁻² )^2+2 x^2 x⁻² x^3 d x & = ( x^2+x⁻² x^3 ) d x= ( 1 x + 1 x^5 ) d x & = |x|- 1 4 x^4 +C aligned

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