How do you integrate #f(x)=(3x^2-x+2)/(4x^2+5)# using the quotient rule?

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Answer 1 · 2016-10-24T16:02:30

There is no quotient rule for integrating. To differentiate, see below.

We can differentiate using the quotient rule (for derivatives).

For #f(x) = u/v# we have, #f'(x) = (u'v-uv')/v^2#.

In this function, #u = 3x^2-x+2#, so #u' = 6x-1#

and #v = 4x^2+5#, so #v' = 8x#.

So, we get

#f'(x) = ((6x-1)(4x^2+5)-(3x^2-x+2)(8x))/(4x^2+5)^2#

# = (4x^2+14x-5)/(4x^2+5)^2#