Question

Integration question:

Answer 1

\[-cosec(6x)\cot(6x)\]

Answer 2

\[-cosec(6x)\cot(6x)\]
\[\frac{ -1 }{ \sin(6x) }*\frac{ \cos (6x) }{\sin (6x)}\]
Integrate \[\frac{ -\cos(6x) }{ \sin^2(6x) }\]

Answer 3

HI!!

Answer 4

Hi Misty1212 I need guidance from here plzz

Answer 5

do you know a function whose derivative is
\[\csc(x)\cot(x)\]?

Answer 6

hint, you should !

Answer 7

if you do not, i can tell you, but i assure you it is in your book under the section of "derivatives of trig functions"

Answer 8

if y=cosec(x)
then y'=-cosec(x)cot(x)

Answer 9

ok you got it

Answer 10

of course you have to adjust for the \(6x\) but that is a mental u - sub
divide by 6 to take care of that

Answer 11

it it clear what i mean?

Answer 12

you need to change the sign, and divide by 6 to get the derivative you want, i.e. \[-\frac{1}{6}\csc(6x)\] will work

Answer 13

yes because when you integrate you tend to divide by the power multiplied by the coefficient of x?

Answer 14

yes it is the chain rule backwards

Answer 15

the check is easy right? take the derivative of
\[-\frac{1}{6}\csc(6x)\] and see that you get the integrand \[\csc(6x)\cot(66x)\]

Answer 16

oops too many sixes, but you get the idea

Answer 17

this is a once step thing which is fantastic thank you!

but if for some reason I decided to make things complicated and go
\[\frac{ -\cos(6x) }{ \sin^2(x) }\]

can i use \[\int\limits \frac{ f'(x) }{ f(x) } \] rule somehow?

Answer 18

you still need the mental u - sub

Answer 19

and it would not be what you wrote, because of the square in the denominator

Answer 20

it would be more like \[\int\frac{f'(x)}{f^2(x)}dx\]

Answer 21

sorry i meant \[\frac{ -\cos(6x) }{ \sin^2(6x) }\]

Answer 22

Sorry I didnt think I made myself very clear
Could I possibly use

\[A \int\limits \frac{ f'(x) }{ f(x) } dx= A \ln \left| fx \right| +c\]

Answer 23

no, as i said, you are missing the square

Answer 24

\[\int\frac{f'(x)}{f^2(x)}dx\]j you will not get the log

Answer 25

oh yea i get it now .. best method is to use the basic rules outlined . Thanks Heaps!
I cant believe i made it so complicated lol

Answer 26

lol it is easy to do with integration
look for the simple first \[\color\magenta\heartsuit\]