Question

integration question

Answer 1

\[\int\limits\limits_{0}^{1} \frac{ x+1 }{ x ^{2}+6x+5 }dx\]

Answer 2

\[x^2+ 6x + 5 = (x+3)^2 -(3)^2 + 5 = (x+3)^2 -9 +5 = (x+3)^2 -1 \]
\[\int\limits \frac{x+1}{(x+3)^{2}-1} \]

Answer 3

Wait. \[\frac{x+1}{(x+5)(x+1)} = \frac{A}{(x+5)} +\frac{B}{(x+1)} \]
Better now. :D

Answer 4

0_o

Answer 5

For A: \(x= -5\) \[\frac{(-5+1)}{(-5+1)} =\frac{-4}{-4}=1 \]

Answer 6

Aren't you forgetting something @Mimi_x3 ?

Answer 7

For B: \(x= -1\) => \(0\)

What am I forgetting?

Answer 8

\[\frac{(x+1)}{(x+5)(x+1)} = \frac{1}{x+5}\]

Answer 9

There is something wrong.

Answer 10

isn't u's and du/dx supposed to come into play about now 0_o?

Answer 11

Oh crap! Sorry!

Answer 12

0_o

Answer 13

So, now \(u= x+5\)

Answer 14

\[\int\limits_{0}^{1}(x+5)^{-1}dx\]

Answer 15

I was right anyway :P
just went the long way.

Answer 16

Ya, exactly. You're so silly :P

Answer 17

That doesn't work hero,
u = x+5

Answer 18

I can make u = x + 5 if I want or not. It doesn't matter. It will still work.

Answer 19

how would u solve (x+5)^-1

Answer 20

\[\ln x+5?\]

Answer 21

no i guess that does not work

Answer 22

\[\int\limits\frac{1}{x+5}dx \]
\[u = x+5 => \frac{du}{dx} = 1 => du = dx \]
\[\int\limits\frac{1}{u} du = \ln(x+5) + C\]
@hero: writing in that form won't work.

Answer 23

\[\ln(|x+5|)\]

Answer 24

I don't need @mimi_x3 ( a kid) to tell me things, lol

Answer 25

@hero right, is absolute value for ln

Answer 26

I am not a kid!!
It's the truth it won't work in the form; of if you want to use that retarded formula.

Answer 27

hero how would u go about doing \[\int\limits_{0}^{1} (x+5)^{-1}\]

Answer 28

Using that form; wont get you anyway; and get lost.

Answer 29

fine mimi, can u tell me your way =/?

Answer 30

She already did. @winterfez, also provided some good steps.

Answer 31

i typed up the solution!!! scroll upp!!

Answer 32

I think I deserve a medal for pointing @mimi_x3 in the right direction.

Answer 33

then with the limits would i be ln 6 - ln 5?

Answer 34

Well, first I was not wrong,I just went the long way. I would have gotten the right anwer without your input.

Secondly, can you please show us how you would integrate \[\int\limits(x+5)^{-1} dx\]

Answer 35

That's top secret info.

Answer 36

Lol, because it's impossible :)

Answer 37

Me want a medal as well!

Answer 38

Nothing is impossible

Answer 39

:D