Definite IntegrationHard

Question

The value of the function f (x) = 1 + x + (ln2t + 2 lnt) dt, where f′(x) vanishes is:

Options

A. e-1
B.0
C.2 e-1
D.1 + 2 e-1

Solution

1 + ln2x + 2ln x = 0
⇒  x =
Let ln t = z     ⇒  1/t dt = dz   ⇒  dt = ez dz
∴  = 1+ =
= 1 + = 1 +

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