Given Definite Integral can be written as:

……(1)

We know that:

And

Let us find the value of 5cosx+3sinx

We know that: 1+tan²x = sec²x

……(2)

Substituting (2) in (1) we get,

Let us assume:

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

……(3)

The upper limit for the Definite Integral:

⇒ t=1……(4)

The lower limit for the Definite Integral:

⇒ t=0……(5)

Substituting (3),(4),(5) in the eq(1) we get,

We need to convert the denominator into standard forms

We know that:

In this problem the values,

Using these values and the standard result, we get,

We know that:

[here f’(x) is derivative of f(x))

We know that: