Help Evaluating integral (x^2 +2)/(x(x^2+5x+8))dx

[GreenPrint]

Easier Way to Evaluate integral (x^2 +2)/(x(x^2+5x+8))dx

see the next post
Evaluate integral (x^2+2)/(x(x^2+5x+8)dx

 

[GreenPrint]

So I got the right answer and wolfram alpha confirms it

http://www.wolframalpha.com/input/?i=d%5B1%2F4ln%28|x|%29-3%2F4ln%28|sqrt%287%29%2F%282sqrt%28%28x%2B+5%2F2%29^2%2B7%2F4%29%29|%29%2B%2825sqrt%287%29%29%2F28cot^%28-1%29%28%282x%2B5%29%2Fsqrt%287%29%29%5D%2Fdx

integral (x^2+2)/(x(x^2+5x+8)dx = -3 ln| sqrt(7)/(2 sqrt( (x+ 5/2)^ 2 + 7/4) ) | + (25*sqrt(7))/7 * cot^(-1)((2x+5)/sqrt(7)) +c

and this was the integration techniques partial fractions section of the book I'm using for calculus two

that was absolutely miserable and took me forever to do
see my work is attached to see how i solved it...

how do i solve this integral in a much easier way using partial fractions what's the easiest way to evaluate this knowing that this is only calculus 2

 

[icystrike]

Easiest way:

$$\int{\frac{f'(x)}{f(x)}=ln(f(x))$$

 

[SammyS]

Easiest way:

$$\int\frac{f\,'(x)}{f(x)}=\ln(f(x))$$

How does this help?

The numerator is not the derivative of the denominator.