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I got one problem

  • Thread starter ludi_srbin
  • Start date
137
0
1. Homework Statement

integral of csc^3(x)cot(x)

2. Homework Equations

I tried using trig identity 1+cot^2(x)=csc^2(x) but I got result where I cancelled my indegrals.

3. The Attempt at a Solution

I tried to substitute the above mentioned indentity for csc^2 but I end up getting -cscx + intgr. cscxcot^3(x). I then substituted for cot^2 but then got to the point where I had -cscx + intgr. csc^(3)xcotx + cscx. At this point everything cancelled out. I also tried substituting sin and cos in the original equation but that didn't get me anywhere neither.
 

Answers and Replies

1,073
1
Try splitting csc3(x)cot(x) into csc2(x)*(csc(x)cot(x)) does that help at all?
 
mjsd
Homework Helper
725
3
write out [tex]\csc^3 (x), \cot(x)[/tex] in terms of [tex]\cos(x), \sin(x)[/tex] and use subsitution or do by inspection :smile:
 
HallsofIvy
Science Advisor
Homework Helper
41,732
893
d_leet's suggestion is simpler (what is the derivative of csc(x)?) while mjsd's suggestion is more "fundamental" (you don't need to know the derivatiive of csc(x), only of cos(x)) but they both give the correct answer.
 

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