After finding the partial fraction decomposition,
∫
\displaystyle \int
∫
11
x
2
−
21
x
−
8
(
x
2
+
2
)
(
x
−
5
)
d
x
\displaystyle \frac{{{11}{x}^{{2}}-{21}{x}-{8}}}{{{\left({x}^{{2}}+{2}\right)}{\left({x}-{5}\right)}}}{\left.{d}{x}\right.}
(
x
2
+
2
)
(
x
−
5
)
11
x
2
−
21
x
−
8
d
x
=
∫
\displaystyle \int
∫
d
x
\displaystyle {\left.{d}{x}\right.}
d
x
Notice you are
NOT
antidifferentiating...just give the decomposition.
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