Question

Evaluate the indefinite integral:
\[\LARGE \int sect(sect+tant)dt\]

Answer 1

scratch that.

Answer 2

here's a tip. Take the derivative of the expression on the inside and see what you get.

Answer 3

When secant is an even power we use u=tanx. here that'd just be du

Answer 4

then we tell our anime wives we love them ♥

Answer 5

@soisoi seems to remember more calculus than me. Sigh
recall that d/dx tan x=sec^2 x
and that d/dx sec x=sec x tan x
expand the expression, and see what you get.

Answer 6

Anyhow the integral of secxtanx = secx right?

Answer 7

Yes, right.

Answer 8

Looks like it's done then.
\[\int\limits sect(sect+tant)dt = \int\limits \sec^2t dt + \int\limits tant)dt =\]
oh god I'm stuck

Answer 9

Tan t can be easily integrated. Express it in terms of sin and cos then do u sub

Answer 10

it's sec x tan x on ur second integral soisoi

Answer 11

I messed up the distribution it was integral secxtanx. Thanks @inkyvoyd

Answer 12

So after distributing we get what soi got..
Then:
\[\LARGE \int sec^2~t~dt=tant+C\]
and \[\LARGE \int tan~t~ dt=-ln|cost|+C\]
So: \[\LARGE tan~t-ln|cosx|+C\]?

Answer 13

nope. use soisoi's correction, and you simply get
sec x+tan x.

Answer 14

+c of course

Answer 15

\[\int\limits\limits sect(sect+tant)dt = \int\limits\limits \sec^2t dt + \int\limits\limits secttant)dt = tant+sect\]

Answer 16

+C

Answer 17

Sorry for flubbing up something so simple lol. And yeah, indefinite integral

Answer 18

Oh, whoops, I see now.

Answer 19

@Luigi0210 , if you don't mind, I would like to have you observe a little interesting tip on your own.
the derivative of sec x+tan x=sec x(sec x+tan x)
what about the derivative of ln|sec x+tan x|?
TRY IT.

Answer 20

Oh, secx?

Answer 21

yeah. Remember that man. I had it on a test once and it was the hardest thing ever without knowing it.

Answer 22

Luckily that didn't catch me on a test. Caught me during practice.

Answer 23

another classic problem is the integral of sec^3 x. Just warning you.

Answer 24

Alright, thanks again everyone. Got calc coming up and just trying to refresh myself on everything.

Answer 25

I got a very good problem from igbiw that i can show you if you are finished self-studying calculus 1 and calculus 2.

Answer 26

Are you up to calc3 at school?

Answer 27

who, me @soisoi

Answer 28

You strike me as someone who's graduated. Luigi

Answer 29

Sure inky.
And I recently graduated HS

Answer 30

Luigi, this one is very difficult and will take a few days, or maybe 4 or 5 hours.
note that you need partial fractions, trig sub, u subt, and a ton of algebra. Ready?

Answer 31

Nope xD