Expert: Paul Klarreich - 3/28/2009

Question
Sorry, the sqrt sign abd multiplication sign on my question came back as ascii code.  Here it is again.

sqrt(csc x) cot^3 x  dx

Thanks

Answer
Questioner:   Brian
Country:  United States
Category:  Calculus
Private:  No
 
Subject:  Calculus Intergration Tables
Question:  Sorry, the sqrt sign abd multiplication sign on my question came back as ascii code.  Here it is again.

sqrt(csc x) cot^3 x  dx

Thanks
.....................................
OK,OK, you really meant it.

How about the same stuff:

De-rationalize (Sorry, I made up that word, but it fits.)


sqrt(csc x) cot^3 x  sqrt(csc x)
------------------- ------------
          1         sqrt(csc x)

csc x cot^3(x)
-----------------
 sqrt(csc x)

csc x cot x (csc^2 x - 1)
--------------------------
 sqrt(csc x)

Now  u = csc x,
du = - csc x cot x

u^2 - 1
-------- =
sqrt(u)

u^(3/2) - u^(-1/2)

That should do it.