I am baffled in solving the following integration problem. Please help!!
∫ 1 / (x^6 – 1) dx
Thanks in advance.
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.
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 ,
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.