Could someone show me step by step how to integrate: tan (x/2)?

I'm not sure if I overlooked any methods.

Question

Could someone show me step by step how to integrate: tan (x/2)?

I'm not sure if I overlooked any methods.

zarkon · Answer

$$\tan(x/2)=\frac{\sin(x/2)}{\cos(x/2)}$$

zarkon · Answer

$$u=\cos(x/2)$$

myininaya · Answer

$$\int\limits_{}^{}\frac{\sin(x/2)}{\cos(x/2)}dx, let u=\cos(x/2)=>du=\frac{-1}{2}\sin(x/2) dx$$

myininaya · Answer

$$=>-2du=\sin(x/2)dx$$

zarkon · Answer

you know you can use \text{} in latex to display regular text in math mode.

then you can get...

$$\int\limits_{}^{}\frac{\sin(x/2)}{\cos(x/2)}dx,\text{ let }u=\cos(x/2)=>du=\frac{-1}{2}\sin(x/2) dx$$

anonymous · Answer

Thank you very much. I got it now.

myininaya · Answer

zarkon so n-spire is the best calculator right?

myininaya · Answer

what model of n-spire?

myininaya · Answer

if i buy one, what should i make sure comes with it?

zarkon · Answer

http://www.datamath.org/Graphing/NSpire_CX_CAS_P1.htm

myininaya · Answer

thanks :)

zarkon · Answer

awesome calculator

zarkon · Answer

I don't have the color one (CX)...I just have the black n white n-spire cas

myininaya · Answer

someone stole my ti83
so i was thinking about investing a new calculator
i love that ti83 too
:(

zarkon · Answer

I have two 83's  (83 and 83+)

myininaya · Answer

but you know they probably really needed the calculator since they are poor

zarkon · Answer

two 82's, and 89, 92+ and my nspire

myininaya · Answer

so i donated but i don't know who too

myininaya · Answer

wow so many

myininaya · Answer

you know i'm starting my phd in applied science this semester?

zarkon · Answer

also have 4 scientific calculators ;)

zarkon · Answer

no graphinf

zarkon · Answer

cool

zarkon · Answer

you have a masters?

myininaya · Answer

i only need 2 lecture classes and the rest is research

myininaya · Answer

yes

zarkon · Answer

awesome

myininaya · Answer

eventhough i can't do algebra sometimes lol

zarkon · Answer

you have an adviser in mind?

myininaya · Answer

yes

zarkon · Answer

good...that is really the most important thing to know :)

myininaya · Answer

so i'm really scared and excited at the same time

zarkon · Answer

is there a specific area you are looking to do research in?

zarkon · Answer

I did mine in bioinformatics

zarkon · Answer

probabilistic modeling

myininaya · Answer

yes 
i asked everyone in the math department hey can we look into some advanced number theory stuff (i wanted to be an expert in that) and no on was interested because no one had expertise in number theory
so i went to the computer department and found someone who does applied cryptography and asked him if he would be interested in theory only and he said yes :)
and so i found my partner in crime

zarkon · Answer

nice

myininaya · Answer

theory of cryptography*

zarkon · Answer

sounds like fun

myininaya · Answer

which is everything i want anyways

anonymous · Answer

wow, color screen

myininaya · Answer

number theory
group theory 
set theory
algebraic structures
abstract algebra

zarkon · Answer

cool

zarkon · Answer

65536 colors

myininaya · Answer

i didn't get into advanced differential equations

myininaya · Answer

also graph theory add that to crypto-list

zarkon · Answer

I've never really studied cryptography so I don't really know what all is involved.

zarkon · Answer

sounds like a lot though

myininaya · Answer

my goal is to eventually construct my own algorithm for encryption 
you know like the RSA

zarkon · Answer

gotcha

myininaya · Answer

i need to test it using statitics 
like see what the probability of it holding its security over a certain time interval

myininaya · Answer

since i'm not a programmer

myininaya · Answer

math is the only way for me to test it

zarkon · Answer

ic

myininaya · Answer

i don't know how i will do that yet using stat

myininaya · Answer

but im sure i will find out how

myininaya · Answer

eventually

zarkon · Answer

I'm sure you will

myininaya · Answer

so everyone else is doing finite element and i think thats gross looking lol

zarkon · Answer

lol

myininaya · Answer

you got any number theorist at your college?

zarkon · Answer

no

myininaya · Answer

is that not a popular choice?

zarkon · Answer

my department is small.

zarkon · Answer

we only have 2 Ph.D.'s in the department :)

zarkon · Answer

me- Mathematical Statistics and the other is abstract algebra (group theory)

myininaya · Answer

sounds like my school
we only have 2 phds as well but one barely teaches because they are an adminstrator 
(the one i teach at)
the one i teach at doesn't have a phd offering of any kind

zarkon · Answer

it is sort of nice since I get to teach most of the upper level classes

myininaya · Answer

i think i would like to teach number theory once i got comfortable with it

zarkon · Answer

the other prof at my college has taught that class...I have not

zarkon · Answer

it is interesting stuff

myininaya · Answer

yes i agree 
i took number theory during the summer one semester at UALR
and i remember some stuff but i totally need a review
my mind doesn't hold very much info anymore :(

myininaya · Answer

i want to take memory pills lol

zarkon · Answer

that would be nice...i need those too

zarkon · Answer

well...good luck and have fun.

myininaya · Answer

later

zarkon · Answer

later