After finding the partial fraction decomposition,

\displaystyle \int 11x221x8(x2+2)(x5)dx\displaystyle \frac{{{11}{x}^{{2}}-{21}{x}-{8}}}{{{\left({x}^{{2}}+{2}\right)}{\left({x}-{5}\right)}}}{\left.{d}{x}\right.} =
\displaystyle \int dx\displaystyle {\left.{d}{x}\right.}


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