# P3 Integration question

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#1
hey, I need help with this question...

integrate cot^4 x

this is what I've done so far: -

cot^4 x = (cot^2 x)(cot^2 x)

since cot^x = cosec^2 x - 1

cot^4 x = (cot^2 x)(cosec^2 x - 1)

so to Integrate cot^4 x, let u = cot x

du/dx = - cosec^2 x

dx = du/(-cosec^2 x)

therefore,

int cot^4 x = [u^2 (cosec^2 x - 1)]/-cosec^2 x . du

now, I dont know how to get rid off the other cosec^2 x....or is this not the correct way of doing it (function and its derivative)

help would be appreciated 0
16 years ago
#2
cot^4 x = (cot^2 x)(cosec^2 x - 1)
You should multiply this out.

See this thread if you're still stuck.
0
16 years ago
#3
You were going the right way by splitting it into (cot^2)(cot^2) and substituting cot^2=cosec^2 -1. I would expand that toget
cot^4 x= (cot^2 x).(cosec^2 x) - (cot^2 x)
Use the same substitution again to get
cot^4 x= (cot^2 x).(cosec^2 x) - (cosec^2 x) +1
Now let u=cotx. du/dx=-cosec^2 x
Go on from there, and you're supposed to get -1/3 (cotx)^3 + cotx +x +C
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