Question

determine the following integral:

equation posted next

Answer 1

\[\int\limits_{}^{}\frac{ e ^{x}+\sec ^{2}x }{ e ^{x}+\tan x }\]

Answer 2

is it \[\frac{ e ^{x}+\tan x }{ e ^{x}+ \frac{ \cos x }{ sin x } }\]

Answer 3

anyone?

Answer 4

put e^x + tan x = u

Answer 5

ok done

Answer 6

That's not correct. But if you do the substitution @hartnn mentioned it should work out.

Answer 7

u get du = e^x +sec^2 x hx
which is your numerator.

Answer 8

use
\(\huge \int \frac{f'(x)}{f(x)}dx=ln|f(x)|+c\)

Answer 9

oh ().o

Answer 10

u get integral of (1/u) du

Answer 11

which is ln|u|+c

Answer 12

I am not understanding this at all. why do you have hx in du = e^x +sec^2 x hx

Answer 13

that was typo, sorry
du = e^x +sec^2 x dx

Answer 14

oh ok. so then ln|e^x+tanx|+c?

Answer 15

thats it :)

Answer 16

Okay, starting from
\[ \int{\frac{e^x+\sec^2(x)}{e^x+\tan(x)}dx} \]
we do the substitution \(u=e^x+\tan(x)\), and since \(du=(e^x+\sec^2(x))dx\), we get
\[ \int{\frac{du}{u}} \]
Now if you do that integral and then substitute back, you get your answer.

Answer 17

lol my brain is asleep today.

Answer 18

Which step don't you understand?

Answer 19

nope got it now dape

Answer 20

Okay :)

Answer 21

but i have got another question about integrals

Answer 22

Go ahead

Answer 23

ill post a new one

Answer 24

@ANTOINETTEs post that as a new question. not in comments.......