Integrating 1/(sinx)^6 dxDate: 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? Does this help? Write back if you'd like to talk about this some 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 |
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