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If the integral Ι = ∫ d x x 10 + x = λ l n x 9 1 + x μ + C , (where, C is the constant of integration) then the value of 1 λ + μ is equal to

Options

  1. A81
  2. B82 9
  3. C18
  4. D8

Correct answer

C. 18

Step-by-step solution

I = ∫ x - 10 1 + x - 9 d x Put 1 + x - 9 = t ⇒ - 9 x - 10 d x = d t ⇒ Ι = ∫ d t - 9 t = - 1 9 ln ⁡ t + C = - 1 9 l n 1 + x - 9 + C = 1 9 ln ⁡ x 9 1 + x 9 + C ⇒ λ = 1 9 , μ = 9 ∴ 1 λ + μ = 9 + 9 = 1 8

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