Question

Find the integral.

Answer 1

\[\large \int\limits \frac{6x+9}{4x^2+4x+5}dx\]Hmm I think we can do a `U sub`, we just have to mess around with it a bit.

Answer 2

i am going to guess annoying partial fractions
just a guess

Answer 3

yeah, i got all mixed up so asking for help... lol

Answer 4

Darn I thought that was going to work XD lol

Answer 5

no, that was a bad guess on my part

Answer 6

i think the u sub idea is better

Answer 7

I can't quite get it to work, hmm.\[\large u=4x^2+4x+5\]\[\large du=8x+4\;dx \qquad \rightarrow \qquad du=\frac{3}{4}(6x+3)dx\]\[\large \frac{4}{3}du=(6x+9-6) \;dx\]

Hmmmmm I don't think it quite works out, cause of that darn dx D:

Answer 8

\[\large \int\limits \frac{6x+9}{4x^2+4x+5}dx\]
\[\large \int\limits \frac{6x+3}{4x^2+4x+5}dx+\large \int\limits \frac{3}{4x^2+4x+5}dx\]\]

Answer 9

Ah yes :P

Answer 10

u sub for the first one, some annoying completing the square for the second

Answer 11

Err +6 on top of the second one.

Answer 12

Understand what's going on albie? :3

Answer 13

i had something different, dont know if this is better though. took out the six at the beginning. had: \[6 \large \int\limits\limits \frac{x+\frac{ 9 }{ 6 }}{4x^2+4x+5}dx \]

then added an eight

Answer 14

umm

Answer 15

\[\frac{ 6 }{ 8} \large \int\limits\limits\limits \frac{8x+\ 8\frac{ 9 }{ 6 }}{4x^2+4x+5}dx \]

Answer 16

yea i understand... separated the equation into two fractions.