I need help with calculus problem integral

Question

anonymous · Answer

$$)\int\limits_{}^{}\frac{ 1 }{ 3 }\sec(\frac{ x }{ 6 })dx$$

anonymous · Answer

I think first using u = x/6 , du = 1/6

anonymous · Answer

then take it out then get 6/3 = 3 integral of sec(u) dx

perl · Answer

theres a trick with solving integral sec x,  multiply top and bottom by sec x + tan x

anonymous · Answer

then 3[ln|secu + tanu|] +c

perl · Answer

right

perl · Answer

and then substitute back

anonymous · Answer

yeah but after that I am trying to simplify it to obtain

anonymous · Answer

$$2\log(\sin(x/12)+\cos(x/12))-2\log(\cos(x/12)-\sin(x/12))+C$$

anonymous · Answer

how can I obtain that from 3[ln|sec(x/6)tan(x/6)|]+C?

perl · Answer

thats a strange expression,

perl · Answer

but you can use a trig product to sum identity

anonymous · Answer

actually its 2[ln|sec(x/6)tan(x/6)|}+C

anonymous · Answer

I got asked by the professor to simplify it as much as possible and I'm trying to get to that

perl · Answer

ok one sec, brb

perl · Answer

wolfram gave me the same expression as your 'professor'

anonymous · Answer

no, that expression is from wolfram and I'm trying to get that since wolfram usually simplifies it as much as possible

perl · Answer

not in this case it doesnt.

perl · Answer

wolfram does not always simplify as much as possible.

anonymous · Answer

ok, so in this case for this problem. The best simplification would just be the answer I got?

perl · Answer

yes. im not sure why wolfram does this

anonymous · Answer

ok, thanks

perl · Answer

wolfram is using an identity here

perl · Answer

which seems to complicate things a bit