Question

Help integrate: cot^3(x)

Answer 1

table that one

Answer 2

∫ tan³(x) dx
= ∫ tan(x)tan²(x) dx
= ∫ tan(x)(sec²(x) - 1) dx
= ∫ tan(x)sec²(x) - tan(x) dx
= ∫ tan(x)sec²(x) dx - ∫tan(x) dx
= ∫ tan(x)sec²(x) dx - ln|sec(x)|

let u = tan(x)
du = sec²(x) dx

= ∫ u du - ln|sec(x)|
= u²/2 - ln|sec(x)| + C

= tan²(x)/2 - ln|sec(x)| + C

Answer 3

\[\text{ recall } \cot^2(x)+1=\csc^2(x)\]

Answer 4

=>\[\cot^2(x)=\csc^2(x)-1\]
now follow what indy did above it will the same process for this integral

Answer 5

how did you cange it to tan^3 x

Answer 6

he didn't
he was giving you an example to follow

Answer 7

\[\int\limits_{}^{}\cot(x)\cot^2(x) dx=\int\limits_{}^{}\cot(x)(\csc^2(x)-1) dx\]

Answer 8

\[=\int\limits_{}^{}\cot(x)\csc^2(x) dx-\int\limits_{}^{}\cot(x) dx\]

Answer 9

okay, i got that far, myininaya, but waht do i do next

Answer 10

for the first one let u=cot(x)=>du=-csc^2(x) dx
second one let u=sin(x)=> du=cos(x) dx

Answer 11

and i like u
you can call your substitution something different for the second one if you like

Answer 12

okay, that actually now is starting to sound Good, let me try it and i will get back to you

Answer 13

i also like u

Answer 14

i mean i don't like u
lol
i mean i don't know you
i mean u as in the substitution u lol

Answer 15

as in u the variable

Answer 16

you dont like me :(

Answer 17

I like u too

Answer 18

hilarious one @ mathsnake

Answer 19

lol stupid u
not you

Answer 20

i don't like u anymore

Answer 21

lol dummy U

Answer 22

its confusing

Answer 23

as in dummy variable

Answer 24

right