hi, is there any method of integrating a hyperbolic or trignometric function whos degree is 4, such as (tanx)^4, (cosechx)^4 WITHOUT resorting to reduction formulae??

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- Apr 7th 2006, 07:24 AMthemintegration
hi, is there any method of integrating a hyperbolic or trignometric function whos degree is 4, such as (tanx)^4, (cosechx)^4 WITHOUT resorting to reduction formulae??

- Apr 8th 2006, 07:21 AMTD!
Sure, there just isn't a "golden recipe" which will be succesfull every time. You'll need to play arround with trig formulas. I'll do one as an example.

Now I'll split the integral in two. The first one is easy since the derivative of tan(x) is exactly secē(x), so:

For the second one; I convert to sin(x) and cos(x):

Splitting the integral in two again gives us simply:

So we conclude, without reduction-formula:

- Apr 8th 2006, 12:54 PMthemreply
thanks, that was great help..i noticed the reduction formula gave effectively the same answer but in a different form.

- Apr 8th 2006, 02:27 PMTD!
Yes, that's perfectly possible and happens very often when you compare 'manual integration' and integration through such reduction formulas.