Evaluate the following Integrals:

Given Definite Integral can be written as:

We know that: 1+ cos2x = 2cos²x and

Let us assume, y = tanx

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

⇒ d(y) = d(tanx)

⇒ dy = sec²xdx……(2)

Upper limit for the Definite Integral:

⇒ y = 1……(3)

The lower limit for the Definite Integral:

⇒ y = 0……(4)

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

We know that:

We know that:

[here f’(x) is derivative of f(x)).