If f α = ∫ 1 α log 10 t 1 + t d t , α > 0 , then f e 3 + f e - 3 is equal to

Step-by-step solution

Given, f α = ∫ 1 α log 10 t 1 + t d t So, f e 3 = ∫ 1 e 3 ln t ln 10 1 + t dt           ⋯ 1 Again f α = ∫ 1 α ln t ln 10 1 + t d t Now let t = 1 x ⇒ x = 1 t ⇒ d t = - 1 x 2 d x So, f α = ∫ 1 1 a - ln n x ln 10 1 + 1 x - 1 x 2 d x ⇒ f α = 1 l n 10 ∫ 1 1 α l n x x x + 1 d x So, f e - 3 = 1 l n 10 ∫ 1 e 3 l n t t t + 1 d t           … 2 Now adding equation 1 and 2 we ge