Matematické Fórum

Skrytý text:


1.)  perform linear transformation on variable so that you get the integral like



2.) substitute    to get



3.) substitute    using  , , to get integral containing polynomials



4.) solve by partial fractions method

you should be prepared for calculations with some nasty coefficients following this way given the coefficients in original integrand function

Skrytý text:


integrand is defined for all as the values of it are strictly positive.

you want to get  in the numerator first

numerator can be expressed as 

so I substituted ,     giving ,  where

getting (after expanding denominator)

Skrytý text:


in last integral from (step 1) I substituted  ,  ,   

getting   

giving       as      given the range for

Skrytý text:


into last integral from (step 2) I substituted
  for    giving  ,  ,  ,  the expressions are put directly into integral above

after rearrangement and calculation of complex roots for polynomial of 4th degree I got to something like this

Skrytý text:


the last integral from (step 3) is ready for calculation using partial fractions method
this is where the real annoying work starts since the coefficients of the polynomials in denominator are
already horrible
and to get to partial fractions you need to solve the system of 6 linear equations with 6 variables with coefficients derived from those (this is where I expected the nasty work in my original post)

I did not proceed with this part but it is proven to be computable