Evaluate the following Integrals:

Given Definite Integral can be written as:

We know that:

We know that: 1+tan²x = sec²x

Let us assume,

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

The upper limit for the Definite Integral:

⇒ y = ∞……(3)

Lower limit for the Definite Integral:

⇒ y = 0……(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)).