Question

I need help understanding an integration problem.
(see attachment)

Answer 1

Here is the part I don't understand.

Answer 2

you distribute the (x^2+2) to (x^2-2)(x^2+2) and the x. therefore in the first one (x^2+2) cancels and the other one is just x/(x^2+2)

=> (x^2-2) + x/(x^2+2)

Answer 3

Hmm, I still quite understand what you are saying. :(

Answer 4

*don't

Answer 5

\[\large \int\limits \frac{(x^2-2)(x^2+2)+x}{(x^2+2)}dx\]You understand up to this part? The next step is actually `2 steps` so I can understand why it was a little confusing.

Answer 6

Yes.

Answer 7

\[\large \int\limits\limits \frac{(x^2-2)(x^2+2)}{(x^2+2)}+\frac{x}{(x^2+2)}dx\]The first step is to write it as two fractions.

Answer 8

ok, makes sense.

Answer 9

Then from there, you have a nice cancellation in the first fraction, see it? :)

Answer 10

Oh! I get it now. Then you just cancel.