Question

∫secu du = ? *proof*

Answer 1

Int (Sec(u)) = Int (1/(cosu) du)

Answer 2

use integration by parts now, i think..

Answer 3

no something much weirder
multiply top and bottom by (sec(u)+tan(u)
then use a sub

Answer 4

multiply top and bottom by (sec u + tan u) then you'll see what happens

Answer 5

Consider:
\[\int\limits \sec{\xi}*\frac{\sec(\xi)+\tan(\xi)}{\sec(\xi)+\tan(\xi)} d \xi=\int\limits \frac{\sec^2(\xi)+\sec(\xi)\tan(\xi)}{\sec(\xi)+\tan(\xi)}d \xi\]
Let:
\[\zeta=\sec(\xi)+\tan(\xi) \implies \frac{d \zeta}{d \xi}=\sec(\xi)\tan(\xi)+\sec^2(\xi) \implies\]
\[d \zeta = \sec(\xi)\tan(\xi)+\sec^2(\xi)d \xi\]
\[\int\limits \frac{d \zeta}{\zeta}=\ln|\zeta|+C=\ln|\sec(\xi)+\tan(\xi)|+C\]
Q.E.D.

Answer 6

\[\int\limits_{}^{}\frac{\sec(u)^2+\sec(u)\tan(u)}{\sec(u)+\tan(u)} du=\int\limits_{}^{}\frac{da}{a}=\ln|a|+C\]

Answer 7

I WAS GETTING THERE JEEZ!!!

Answer 8

lol sorry male
(its been awhile since i seen you)

Answer 9

I know :D Whats up!?

Answer 10

where you been?

Answer 11

like the
\[\zeta, \xi,\] andso one

Answer 12

okay so im a bit lost...
would one of you be able to post all the work showing how to get the final answer? please and thank you

Answer 13

male did

Answer 14

what do you not understand about it?

Answer 15

the symbol he has simply stands for u?

Answer 16

yes he was just trying to be fancy

Answer 17

I just like using different symbols is all. "U-substitution" is just a generic variable that mathematicians like to use alot. You can use anything, even a small drawing of an acorn O.O

Answer 18

okay, thank youu

Answer 19

or a smiley face

Answer 20

I do that sometimes

Answer 21

@satellite73 I've just been busy v.v