Question

How do you integrate `y=x/(x^2+1)` using the quotient rule?

Answer 1

Do you mean Differentiate?

Explanation:

To integrate you might be able to use partial fraction but differentiation using the quotient rule will give you:

`(x'(x^2+1)-(x^2+1)'(x))/(x^2+1)^2`=`(x^2+1-3x)/(x^2+1)^2`

`y'`=`(x^2-3x+1)/(x^4+2x^2+1)`