After finding the partial fraction decomposition,

\displaystyle \int 8x220x48(x2+2)(x7)dx\displaystyle \frac{{{8}{x}^{{2}}-{20}{x}-{48}}}{{{\left({x}^{{2}}+{2}\right)}{\left({x}-{7}\right)}}}{\left.{d}{x}\right.} =
\displaystyle \int dx\displaystyle {\left.{d}{x}\right.}


Notice you are NOT antidifferentiating...just give the decomposition.