Given Definite Integral can be written as:

Let us assume x = tany

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

⇒ d(x) = d(tany)

⇒ dx = sec²ydy……-(2)

Then

We know that:

Now,

Upper limit for the Definite Integral:

⇒ x = 1 ⇒ y = tan^-1(1)

Lower limit for the Definite Integral:

⇒ x = 0 ⇒ y = tan^-1(0)

⇒ y = 0…… (5)

Substituting (2),(3),(4),(5) in (1) we get,

We know that the By-partss integration is:

Now applying by parts Integration:

We know that: ∫ sec²xdx = tanx + C

We know that:

[here f’(x) is derivative of f(x))

We know that: ∫ tanxdx = -log(cosx) + C

We know that: log(a^b) = bloga