Question

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

Answer 1

There is no quotient rule for integrating.

Explanation:

There is a quotient rule for differentiating, perhaps that is what was meant.

`d/dx(u/v) = (u'v-uv')/v^2`

In this case `u = lnx`, so `u' = 1/x`

and `v = 1+x^2`

`d/dx((lnx)/(1+x^2)) = (1/x(1+x^2)-(lnx)(2x))/(1+x^2)^2`

`= (1+x^2-2x^2lnx)/(x(1+x^2)^2)`