Integrate the given function.

To integrate the function , we can use a simple substitution method. Let’s set . Then, the differential , or . Substituting these into the integral gives us:

Substituting back , we get:

If you want to solidify your understanding, try applying the same technique to different functions involving linear expressions in the denominator. It can be enlightening how the same principles yield varying results!

Also, it’s fascinating to explore how integrals like these have real-world implications. For example, this type of function commonly appears in situations involving exponential growth and decay in fields such as physics and economics, where understanding rates of change is crucial.