Evaluate the following Integrals:

Given Definite Integral can be written as:

We know that:

Substituting these value in (1) we get,

We know that: 1+tan²x = sec²x

Let us assume,

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

Upper limit for the Definite Integral:

Lower limit for the Definite Integral:

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

We know that:

We know that:

[here f’(x) is derivative of f(x)).

We know that: Log = log(a) – log(b)