## ratherbcoding one year ago 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

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

2. phi

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"