Find the anti derivative of f'(x)= (2+x^2)/(1+x^2)

  • Thread starter skyturnred
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  • #1
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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?
 

Answers and Replies

  • #2
gb7nash
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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?
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.
 
  • #3
Ray Vickson
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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.
You could also write [tex] \frac{2+x^2}{1+x^2} = 1 + \frac{1}{1+x^2}. [/tex]

RGV
 
  • #4
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Thank you to both of you for your help, both of you helped me solve this and other similar questions.
 

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