After finding the partial fraction decomposition,
∫
\displaystyle \int
∫
8
x
2
−
20
x
−
48
(
x
2
+
2
)
(
x
−
7
)
d
x
\displaystyle \frac{{{8}{x}^{{2}}-{20}{x}-{48}}}{{{\left({x}^{{2}}+{2}\right)}{\left({x}-{7}\right)}}}{\left.{d}{x}\right.}
(
x
2
+
2
)
(
x
−
7
)
8
x
2
−
20
x
−
48
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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