Use partial fraction decomposition to evaluate the integral:
∫
8
t
3
+
19
t
2
+
52
t
+
90
2
t
3
+
5
t
2
+
6
t
+
15
d
t
\displaystyle \int\frac{{{8}{t}^{{3}}+{19}{t}^{{2}}+{52}{t}+{90}}}{{{2}{t}^{{3}}+{5}{t}^{{2}}+{6}{t}+{15}}}{\left.{d}{t}\right.}
∫
2
t
3
+
5
t
2
+
6
t
+
15
8
t
3
+
19
t
2
+
52
t
+
90
d
t
=
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