The discussion revolves around finding the antiderivative of the function f'(x) = (2+x^2)/(1+x^2). Participants are exploring methods of integration, particularly focusing on whether integration by parts is necessary or if there are alternative approaches available.
There is an ongoing exploration of different methods to approach the problem. Some participants have provided insights into simplifying the expression, which may guide others in their understanding of the integration process. However, no consensus has been reached regarding the best method to use.
Participants note that integration by parts may not have been covered in their coursework yet, which adds a layer of complexity to their attempts at solving the problem.
skyturnred said:Homework Statement
f'(x)= (2+x^2)/(1+x^2), find f(x).
Homework Equations
The Attempt at a Solution
I am pretty sure you have to use integration by parts... but I don't think we learned it yet. Is there a way to do this without using integration by parts? If not, how would I use integration by parts for his question?
gb7nash said:Well, [itex]\frac{2+x^2}{1+x^2} = \frac{2}{1+x^2}+\frac{x^2}{1+x^2}[/itex]
If you know what the integral of [itex]\frac{1}{1+x^2}[/itex] is, the first part is easy. The second part is simple as well, if you recognize what to do first before integrating.