Question

Integrate cot x csc^2x dx

Answer 1

I'm trying the substitution u = cot x
and using the identity csc^2 x = 1 + cot^2 x

Answer 2

hold on its cot^x = 1 + csc^2 x right?

Answer 3

\[\int\limits_{}^{}\cot x \csc ^2x dx=\int\limits_{}^{}\frac{ cosx }{ \sin^3x }dx\]

Answer 4

and how would you proceed from there?

Answer 5

if u = cot(x)

what is du?

Answer 6

u sub\[u=\sin x\]\[du=\cos x dx\]\[dx=\frac{ 1 }{ \cos x }\]

Answer 7

du/dx ln sin x

Answer 8

thats where i got stuck

Answer 9

i recall

D[tan(x)] = sec^2(x)

D[cot(x)] = -csc^2(x)

Answer 10

\[\int\limits_{}^{}\frac{ \cos x }{ u^3 }\frac{ 1 }{ \cos x }du\]

Answer 11

\[\int cot(x)~csc^2(x)~dx\implies -\int u~du\]

Answer 12

ya wanna take over am?

Answer 13

ah - i was using ln sin x instead of -csc^2 x

i can see it now

Answer 14

take over? nah, just a perspective :)

Answer 15

heh i have my own problems to solve too actually, not working too well

Answer 16

welsh is a smart fella :)

Answer 17

but i cant put it here cause it doesnt belong to maths

Answer 18

yes I see it now thanks for your help

Answer 19

I looked up the integral instead of the derivative!!!! that wasn't so smart!!!

Answer 20

lol

Answer 21

lol that happens alot

Answer 22

ty both

Answer 23

engineering department seems dead