Expert: Paul Klarreich - 3/28/2009

Question
How would you approach evaluating this integral?

intergaral of √(csc x)∙cot^3 x dx

I have tried integration by parts but can not find the right u and dv.

Thanks for the help

Answer
Questioner:   Brian
Country:  United States
Category:  Calculus
Private:  No
 
Subject:  Calculus Intergration Tables
Question:  How would you approach evaluating this integral?

integral of √(csc x)∙cot^3 x dx

I have tried integration by parts but can not find the right u and dv.

Thanks for the help
--------------------------------
This came out as sqrt(csc x), but I don't think you meant that.

If it is:

{
| csc x cot^3 x dx
}

Then  cot^3(x) = cot^2(x) cot x = (csc^2(x) - 1) cot x

 
{
| csc x (csc^2(x) - 1) cot x dx
}


{
| csc x cot x (csc^2(x) - 1)  dx
}

Now  u = csc(x) should do the job.

Now, if you really meant ....