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quotient rule may be

write x^2+1 as x^2-1+2, make two basic integrals and solve

ha i was just going to suggest partial fractions
1-x^2 = (1-x)(1+x)

oh right split it into 2 fractions first

This kind of idea comes from experience I guess?

yes, it takes some practice to get the routine, but consider it very easy integral...:D

ok, thx for your help :)

if you've got some more problems with integrals hit me now :D

Do you want to see it with partial fractions?
it's not very hard

Yes, might be a nice to see a different approach.

OK, I didn't know that they must do it like that :D

Can I do this partial fractions stuff also without changing x^2+1 to x^2-1+2?

the degree of the numerator*