Question

integral of dx/(3x^2+1)

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

it should be some type of arctan

Answer 3

let me solve it one sec

Answer 4

okay

Answer 5

http://www.wolframalpha.com/input/?i=integral+of+dx%2F%283x^2%2B1%29

Answer 6

arctan(sqrt(3)x)/sqrt(3)

Answer 7

oooooo I get it...lol

Answer 8

Okay! How do I give you a medal? lol

Answer 9

bring three under the square, and chain rule backwards

Answer 10

click good answer by my name on one of the posts

Answer 11

where is the good answer? lol

Answer 12

look at the grey bar with my name and picture and follow it to the right

Answer 13

this should not be this difficult I'm sorry I'm new here

Answer 14

haha its ok im pretty new here too. if you can't find it right now don't worry about it :)

Answer 15

alright thanks! I'll still look for it

Answer 16

any other questions while im here?

Answer 17

hmmm yesssss

Answer 18

integral x^5ln(3x)dx

Answer 19

like this ?
\[\int\limits_{}^{}x^{5}\ln(3x)dx\]

Answer 20

yea

Answer 21

k let me work it out im geussing its by parts

Answer 22

k yeah it is. Do you know integration by parts?

Answer 23

ummmm kind of

Answer 24

ok well I'll give you the equation:

\[\int\limits_{}^{}udv=uv-\int\limits_{}^{}vdu\]

Answer 25

alrighty

Answer 26

Oh okay...

Answer 27

so in your problem we choose ln(3x)=u, x^5=dv
differentiate u and integrate dv

Answer 28

okay...trying this right now...

Answer 29

du=1/x
v=x^6/6
so using the by parts formula now you have:
\[\frac{x^{6}\ln(3x)}{6}-\int\limits_{}^{}\frac{x^{5}}{6}dx\]

Answer 30

Alright...

Answer 31

got that...lol

Answer 32

yep so you reduce it to an integral we can do more easily like the one above

Answer 33

yup

Answer 34

when I simplified I got

\[\frac{x^{6}(6\ln(3x)-1)}{36}+C\]

Answer 35

okay would you get...1/6x^6ln(3x) - (1/36)x^6?

Answer 36

yep that is the same

Answer 37

lol okay same thing I got

Answer 38

thanks :D

Answer 39

no problem

Answer 40

where the heck is this good anser button -.- I'm getting annoyed lol

Answer 41

I'm sorry I can't find it >.<

Answer 42

look at the post where I typed "no problem" it is in the upper right corner of that box

Answer 43

well it should be at least haha

Answer 44

it just says 0 medals for this answer o.o

Answer 45

theres no button directly to the right of that in blue?

Answer 46

nope o.o

Answer 47

there isnt one on any of the posts? there shouldnt be one for your own, but only for others' posts

Answer 48

no I don't see anything...lol

Answer 49

weird, thats where it is for me.

Answer 50

let me google this LOL

Answer 51

i just gave you one haha

Answer 52

are you a member?

Answer 53

NOW I have it

Answer 54

oh i geuss you need a medal to give one?

Answer 55

lol I just need to refresh the page lol

Answer 56

oh or maybe that too

Answer 57

any more integrals?

Answer 58

let me check...do you remember anything about series?

Answer 59

yeah I know some about them

Answer 60

We studied them a bit in complex analysis recently

Answer 61

Ooo okay

Answer 62

oh here is an integral...dy/dx+xy=x

Answer 63

y(0)=1/2

Answer 64

oh a diff equation. k give me a sec

Answer 65

it is seperable.

write dy/dx=x-xy=x(1-y)
dy/(1-y)=xdx. Integrate both sides

Answer 66

okay...

Answer 67

so we get -ln(1-y)=x^2/2+C
ln(1-y)=-x^2/2+C (C is some constant sign doesnt matter)

1-y=Ce^(-x^2/2)
y=1+Ce^(-x^2/2)

use the initital condition to find C

y(0)=1/2

1/2=1+C
C=-1/2

y=1-(1/2)e^(-x^2/2)

Answer 68

Oooo so you want to put one side over the other? and then integrate

Answer 69

you want to get the y terms with dy and x terms with dx so you can integrate both sides

Answer 70

Ooo okay

Answer 71

if you can do this it is called a seperable equation

Answer 72

that should be enough! :) thank you very much

Answer 73

lol this is a review...but I don't remember lol

Answer 74

there is a lot of material in calculus

Answer 75

do you want to do one series or good for now?

Answer 76

Ummmm good for now :)

Answer 77

k talk to you later

Answer 78

Thank you very much! Tuly appreciate it

Answer 79

you're welcome