I have question about one integral

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SUMMARY

The integral ∫[1/(1+x^2)^2] dx can be solved effectively using a combination of substitution and integration by parts. The recommended substitution is u = 1/(1+x^2), which simplifies the integral. After finding du, the next step involves expressing x in terms of u to facilitate the integration process. This method provides a clear pathway to arrive at the solution.

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The Attempt at a Solution



Thanks in advance for your help...


∫[1/(1+x^2)^2] dx
 
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What did you try?

Did you try integration by parts, substitution?
 
I managed to get it by using substitution and then parts. Try making u=1/(1+x^2) and then when you get du, use u=1/(1+x^2) to solve for x to replace x with u. After that, use parts. Hope that helps I can give a more detailed answer if you still are having trouble.
 

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