/sci/ - Science & Math

[Anonymous No.8825021]

I'm taking calc 2 and this was one of the challenge homework problems.
I've tried to u sub all the formulas I remember from trig, but can't seem to get it

integral 1/(1+2 cos(x)) dx

[Anonymous No.8825022]

I forgot to mention that it is indefinite

[Anonymous No.8825073]

I know sci is a slow board, but is anyone trying this out? It's due tomorrow

[Anonymous No.8825094]

>>8825021
Calc 3 student here.

Gave it a try and couldn't do it. Used an integral calculator and find that to get a substitution he used this technique:

https://en.wikipedia.org/wiki/Tangent_half-angle_substitution

After that then he did partial fractions and u-sub which I assume is business as usual for you. Given that this tangent half angle wasn't covered for me back then and that it seems it hasn't been covered for you either, I suppose that this being homework implies you had to research and find out about a technique like this.

Well, now you did. So use it and find out the substitution.

[Anonymous No.8825134]

>>8825094
>>8825021
Reporting back.

I did the integral with this technique and it fucking works like magic. Just use the identity
[math] cosx = \frac{1 - tan(\frac{x}{2})^2}{1 + tan(\frac{x}{2})^2} [/math] and then set [math] u = tan(\frac{x}{2})^2 [/math]

Do the substitution. Then you'll have to do a little algebra because you get a soup of u's but you can handle it and reduce it a lot until you reach the form of an integral that you probably already know how to deal with.

[Anonymous No.8825137]

>>8825134
>>8825021
Wait, no. use [math] u = tan(\frac{x}{2}) [/math]