Question

evaluate the integral of sec^2(x)/sqrt(1+tan(x) Show work?

Answer 1

@Alexkwkwl still need help

Answer 2

Yes please

Answer 3

So what are your thoughts

Answer 4

let's just make sure we have the right integral \[\int \frac{\sec^2x}{\sqrt{1+\tan x}}dx\]

Answer 5

is this what you have

Answer 6

Yes

Answer 7

how about a sub in there?

Answer 8

A sub?

Answer 9

substitution

Answer 10

No

Answer 11

why not?

Answer 12

Oh you mean like 1/cos

Answer 13

this sub works good \[u=1+\tan x\]

Answer 14

\[du=\sec^2x dx \]

Answer 15

you can see it now?

Answer 16

Wait And then what do you do

Answer 17

you substitute \(\sec^2x dx\) for \(du\)

Answer 18

Yes i know that

Answer 19

and \(1+\tan x \) for u

Answer 20

then work the integral with u

Answer 21

so?

Answer 22

this is what you get \[\int \frac{du}{ \sqrt{u}}\]

Answer 23

you should be able to integrate this one easily

Answer 24

2?

Answer 25

what you mean by two?
remember indefinite integral gives a family of functions
meaning an anti-derivative with a constant C

Answer 26

you should not get a numerical value

Answer 27

2 times sqrtu +c

Answer 28

yes! now revert back to 1+tanx

Answer 29

remember that we set u=1+tanx

Answer 30

2(1+Tanx) +C

Answer 31

no

Answer 32

you forgot something

Answer 33

Oh the sqrt lol duh

Answer 34

yeah

Answer 35

That's it??

Answer 36

yep

Answer 37

Omg yay thank you so much

Answer 38

yeah you doing great :)
you are welcome