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Manipal MET2010MathematicsIndefinite Integration

x^2+4 x^4+16 d x is equal to

Options

  1. A1 2 2 ⁻¹ ( x^2+4 2 x )+c
  2. B1 2 2 ⁻¹ ( x^2-4 2 2 x )+c
  3. C1 2 2 ⁻¹ ( x^2+4 2 2 x )+c
  4. D1 2 ⁻¹ ( x^2-4 2 x )+c

Correct answer

B. 1 2 2 ⁻¹ ( x^2-4 2 2 x )+c

Step-by-step solution

x^2+4 x^4+16 d x= 1+ 4 x^2 x^2+ 16 x^2 d x= d (x- 4 x ) (x- 4 x )^2+8 = d t t^2+(2 2 )^2 , where t=x- 4 x = 1 2 2 ⁻¹ ( x^2-4 2 2 x )+c

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