Associated Topics || Dr. Math Home || Search Dr. Math

### Integrating 1/(sinx)^6 dx

Date: 02/25/2002 at 05:48:55
From: Ehab Nassif
Subject: Integration

What is the integration of 1/(sinx)^6 dx ?

Thanks a lot for your kindness.

Date: 02/26/2002 at 19:35:16
From: Doctor Jubal
Subject: Re: Integration

Hi Ehab,

Thanks for writing Dr. Math.

Here's a hint to get you started.

It would be a lot easier to integrate something like

/  cosx dx
| ---------
/ (sinx)^6

because then we could make the substitution u = sinx, du = cosx dx,
and be left with an elementary integral. So it would be nice if we
could somehow get a cosine in there.

To do this, note that

1         (sinx)^2     1 - (cosx)^2
---------- = ---------- = --------------
(sinx)^4     (sinx)^6       (sinx)^6

so

1            1         (cosx)^2
---------- = ---------- + ----------
(sinx)^6     (sinx)^4     (sinx)^6

and the integral becomes

/    dx       /    dx       / (cosx)^2 dx
| --------- = | --------- + | ------------
/ (sinx)^6    / (sinx)^4    /   (sinx)^6

Of these two integrals, the right one can be integrated by parts. How
do you suppose the left one might be simplifed?

more, or if you have any other questions.

- Doctor Jubal, The Math Forum
http://mathforum.org/dr.math/

Date: 03/03/2002 at 06:38:08
From: Ehab Nassif
Subject: Integration

Thanks a lot for your solution. I think I can proceed by myself with
the rest of the steps.

Best regards,
Ehab Nassif

Associated Topics:
High School Calculus

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search