Question

Can someone explain to me what's happening in this final step? I've seen the answer, but I don't undertstand how to get it! http://imgur.com/GSuuI0l

Answer 1

In the numerator there is derivative of the denominator so we can apply ln( ) law

Answer 2

if you multiply the top by 3, you get exactly the derivative of the bottom

so put a ⅓ out front , and multiply the top by 3
you now have
\[ \frac{1}{3} \int \frac{du}{u} = \frac{1}{3}\ln(u) \]

notice we can write the above as
\[ \frac{1}{3} \int \frac{du}{u} = \int \frac{du}{3u} \]

it looks like they want to see
3(x^3+ 6x^2 +3x+8) or
3x^3 +18x^2 + 9x + 24
in the "box"