Given Definite Integral can be assumed as:

……(1)

Let us assume y = 1 + log(x)

Differentiating w.r.t x on both sides we get

⇒ d(y) = d(1 + log( x ))

……(2)

Lower limit for Definite Integral:

⇒ x = 1 ⇒ y = 1 + log 1

⇒ y = 1 ……(3)

Upper limit for Definite Integral:

⇒ x = 2 ⇒ y = 1 + log2

⇒ y = 1 + log2 ……(4)

Substituting (2),(3),(4) in the eq(1) we get,

We know that:

We know that:

[here f’(x) is derivative of f(x))

We know that loge=1 and loga+logb=logab