integrate (2(x^2)-9x-9))/(x^3-9x)

It's an integrating rational functions by partial fractions problem...I'll just cut to the chase and give you the answer I got as compared to the book's answer

My answer: ln|x|+2ln|x+3|-ln|x-3|+C

Book answer: ln|(x(x+3)^2)/(x-3)|+C

Is this the same answer but they just put in differently? Or did I miss something?

Question

integrate (2(x^2)-9x-9))/(x^3-9x)

It's an integrating rational functions by partial fractions problem...I'll just cut to the chase and give you the answer I got as compared to the book's answer

My answer: ln|x|+2ln|x+3|-ln|x-3|+C

Book answer: ln|(x(x+3)^2)/(x-3)|+C

Is this the same answer but they just put in differently? Or did I miss something?

abb0t · Answer

It looks the same to me.

abb0t · Answer

$$\ln(a)+\ln(b) = \ln(ab)$$
also: $$\ln(b)-\ln(a) = \ln(\frac{ a }{ b })$$

anonymous · Answer

Gotcha, so they just took it a step further then. Thanks

abb0t · Answer

Often to make it look "neater". But both answers should be find on an exam. Unless they ask for it to be completely simplified. But I'm assuming this is for Calculus course in which case, it's assumed that you have completely mastered algebra by now.