Integration By Parts

Step 1: Simplify the Integral

We are given:

Let's try to rewrite the integrand in a form that is easier to integrate. Divide both numerator and denominator by :

This doesn't simplify it.

Let

So, let's try integration by parts. Rewrite as:

Now, we will perform integration by parts:

Let and

First, find du:

Now, find v. Since , we have:

Let then

Step 2: Apply Integration by Parts

Using integration by parts, we have:

Step 3: Evaluate the Remaining Integral

We know that

So, we have:

Step 4: Identify f(x)

We are given that . Comparing this with our result:

Conclusion:

The function f(x) is: