If the integral I = ∫ e 5 ln ⁡ x x 6 + 1 - 1 d x = ln ⁡ x 6 + 1 + C , (where, C is the constant of integration) then the value of 1 λ is

Question

If the integral I = ∫ e 5 ln ⁡ x x 6 + 1 - 1 d x = ln ⁡ x 6 + 1 + C , (where, C is the constant of integration) then the value of 1 λ is,

MARKS App · Accepted Answer

The integral I = ∫ e 5 ln ⁡ x x 6 + 1 - 1 d x I = ∫ e ln ⁡ x 5 x 6 + 1 d x = ∫ x 5 x 6 + 1 d x = 1 6 ∫ 6 x 5 d x x 6 + 1 Put x 6 + 1 = t 6 x 5 d x = d t ⇒ I = 1 6 ∫ d t t = 1 6 ln ⁡ t + C ⇒ I = 1 6 ln ⁡ x 6 + 1 + C ⇒ λ = 1 6 ⇒ 1 λ = 6

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