How does the int get from that step to this step?

[frasifrasi]

Book ex: We were given integral of $$\frac{sqrt of x + 4}{x}$$/x dx

with the substitution u = sqrt{x + 4}
--> u^2 = x + 4 and x = u^2 - 4
--> dx = 2u du

and the int becomes 2*int of $$\frac{u^2}{u^2 - 4}$$du

But how does it go from that to the next step:

2 int of 1 + $$\frac{4}{u^2 - 4}$$du ?

 

[Proggle]

You add and subtract 4 to the numerator and regroup.

(u^2+4-4)/(u^2 -4) = (u^2-4)/(u^2-4) + 4/(u^2-4) = 1 + 4/(u^2-4)

 

[rocomath]

i'm really confused as to what your original problem is

$$\int\frac{\frac{\sqrt{x+4}}{x}}{x}}dx$$

that?

 

[frasifrasi]

is the integral of sqrt (x+4)/x dx -- sorry for the confusion... And how can the book not explain something like that?!? If i see james stewart on the street I am going to fling pebles at him man.

 

[rocomath]

i actually like his textbook, what ch./sect. is this?

 

[Saladsamurai]

is the integral of sqrt (x+4)/x dx -- sorry for the confusion... And how can the book not explain something like that?!? If i see james stewart on the street I am going to fling pebles at him man.

:rofl: Pebbles?! I guess that'll learn him.