integration question... (1 Viewer)

[*Ninny-mole*]

Okay, this is really easy stuff, but i can't get it right and I can't figure out why. The question is:
( 3 x^2 + 5 dx
2 ) x^2

(in words, integrate, or get the area between 2 and 3, for the function x squared plus five, all over x squared).
I thought that to integrate fractions like this you did log of denominator
f ' (x) of denominator

But, in doing that, I have gotten [ (x^2 + 5) log x^5 ] 3
[ 2x ] 2

That is, my answer is in words, (x squared plus 5) log x to the power of 5, all over 2x.
Does that make sense to everyone? The top line is meant to cancel the pronumerals in the denominator but it doesn't...please help me, it's bugging me....

 

[SoulSearcher]

Split the fraction, makes it a lot easier to work out. And the integral isn't a log function for this particular question.
(x²+5)/x² = 1 + 5/x²
Therefore
int. [(x²+5)/x²] (3->2) dx
= int. [1 + 5/x²] (3->2) dx
= [x - 5/x] (3->2)
= (3-5/3) - (2-5/2)
= 4/3 - (-1/2)
= 4/3 + 1/2
= 11/6 units²

 

[*Ninny-mole*]

Okay I don't know how you did that so fast, but thankyou so much