Antiderivatives

[CoreyyV]

So I have this question:
Find f(x) so that ∫f(x)dx =1/2ln(x^2+ 1) +C

The answer that I got was:
f(x) = x/(x^2+1)
The reasoning behind it was because I know that f(x) = g'(x). So I found the derivative to the original equation. My question is if I did this correctly. I'm asking because it seems like the question was too easy, or I just messed up finding the derivative of : 1/2ln(x^2+1)+C.

Any help would be appreciated!

 

[Steven G]

I will not check your answer for you. I prefer that you check your own answer and see if you get the desired results. If you don't then please post back with your work.

You claim that ∫x/(x^2+1)dx =1/2ln(x^2+ 1) +C. To verify this you must compute the derivative of 1/2ln(x^2+ 1) +C and see if you get back x/(x^2+1).

If you don't and can't find your error then please post back showing your work and we'll help you find your error!

 

[CoreyyV]

I will not check your answer for you. I prefer that you check your own answer and see if you get the desired results. If you don't then please post back with your work.

You claim that ∫x/(x^2+1)dx =1/2ln(x^2+ 1) +C. To verify this you must compute the derivative of 1/2ln(x^2+ 1) +C and see if you get back x/(x^2+1).

If you don't and can't find your error then please post back showing your work and we'll help you find your error!

My apologies, Jomo.

 

[Steven G]

My apologies, Jomo.

No need to apologize. You are a student of this website and as a result you come first. I could have told you that you are right or wrong but will that have helped you know that you are correct the next time?

To verify that the answer to any integral is correct, I want you to know that the derivative of your answer should equal the integrand (the function that you are integrating). That information will help you much more than my saying that you are correct. I also asked you twice to post back with your work if you are having trouble.

I will tell you that the derivative of 1/2ln(x^2+ 1) +C is x/(x^2+1) so you did get the correct answer.

 

[CoreyyV]

I wasn't necessarily having trouble and as I was looking over my work, I was fairly certain that I had found the correct derivative. My concern was that I was missing a step in the question, something that I forgot. I wasn't really looking to see if I had the correct answer, the main reason as to why I was asking was because I wanted to see if I was going about solving the question correctly and if so, then I could check for myself to see if the answer I got was correct. I did however forget about what you said, in that checking your solution is as simple as computing the derivative of the integrand (thank you for this vocabulary because I didn't know before!).

Thank you for the help!