I am baffled in solving the following integration problem. Please help!!

∫ 1 / (x^6 – 1) dx

Thanks in advance.

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- December 20th 2009, 09:39 PMniza baffling integral
I am baffled in solving the following integration problem. Please help!!

∫ 1 / (x^6 – 1) dx

Thanks in advance. - December 20th 2009, 11:29 PMadkinsjr
Are you familiar with the method of partial fractions? Notice that the denominator is the difference of two squares . Now use the formulae for the cubes. You can write that out as

You should be able to apply the method of partial fractions for the case when the denominator contains irreducible quadratic factors. - December 21st 2009, 03:38 AMsimplependulum
Here's my method , it is for those who HATE the method of partial fraction ( but i am not the one )

the integral

the first one we just need to substitute and finally obtain

you may think that we may need to apply partial fraction to solve the second part but if we consider

Divide the numerator and the denominator by

then substitute

the integral becomes

now consider

do the same thing above but sub. this time , we can get

we have

and

,

therefore ,

- December 22nd 2009, 08:31 AMnizThanks
Thanks adkinsjr and simplependulum!! Actually I was hoping for some kind of trigonometric substitution to manipulate the integrand. Like for (x^2 -1) substituting x= secy etc.. I guess there are none such solutions right? Anyway, thanks guys.. Thanks simplependulum for the smart manipulation of the integrand..that was clever.