Question

Integration!
\[\int \frac{x+5}{2x + 3} dx\]

Answer 1

again, I suggest: long division first

Answer 2

Break it in half or not?
\[\int \frac{x}{2x + 3} + \frac{5}{2x + 3} dx\]

Answer 3

why? you are always go on that way?

Answer 4

whenever you see the degree of numerator > or equal the degree of denominator, the first thing you should do is take long division.

Answer 5

hey!! or you don't know how to do it? aha!! if so, you just ask.

Answer 6

Sorry, I got pinged by another question. I'm still here. :)

Answer 7

Anyway, yeah, I tend to go for the breaking or the easy substitutions because I'm not good at polynomial division.

Answer 8

so, just practice, it's not hard. go ahead, show me your long division. I can check or correct if you have a mistake

Answer 9

Ok... so I need to make a "fake" 2x + 3 in the numerator, right?
By writing something like \(\frac{1}{2}(2x + 3) - 1.5 + 5 \)

Answer 10

I take it the thing I was doing was... some other thing entirely?

Answer 11

I am sorry, let me explain

Answer 12

Thank you. :)

Answer 13

Oh, that is really nice! Medal for you! Two if I could!

Answer 14

It's actually similar to what I was doing then. Just totally different thought process to get there. Thank you!

Answer 15

\[\int \frac{1}{2} - \frac{7}{4x + 6} dx\]\[\frac{x}{2} - 7 \int \frac{1}{4x + 6} dx\]
\(u = 4x + 6\)
\(du = 4 dx\)
\[\frac{x}{2} - \frac{7}{4}\ln |4x+6| + C \]