Given Definite Integral can be written as:

……(1)

Let us assume y = logx

Differentiating w.r.t x on both sides

⇒ d(y) = d(logx)

……(2)

Upper limit for the Definite Integral:

⇒ x = 3 ⇒ y = log(3)

⇒ y = log3……(3)

Lower limit for the Definite Integral:

⇒ x = 1 ⇒ y = log(1)

⇒ y = 0……(4)

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

We know that ∫ cos x dx = sin x + c

We know that:

here f’(x) is derivative of f(x))

⇒ I(x) = sin(log3) – sin(0)

⇒ I(x) = sin(log3) – 0

⇒ I(x) = sin(log3)