Consider the indefinite integral
∫
5
x
3
+
9
x
2
+
64
x
+
96
x
4
+
16
x
2
d
x
\displaystyle \int{\frac{{{5}{x}^{{3}}+{9}{x}^{{2}}+{64}{x}+{96}}}{{{x}^{{4}}+{16}{x}^{{2}}}}}{\left.{d}{x}\right.}
∫
x
4
+
16
x
2
5
x
3
+
9
x
2
+
64
x
+
96
d
x
Then the integrand has partial fractions decomposition
a
x
2
+
b
x
+
c
x
+
d
x
2
+
16
\displaystyle {\frac{{{a}}}{{{x}^{{2}}}}}+{\frac{{{b}}}{{{x}}}}+{\frac{{{c}{x}+{d}}}{{{x}^{{2}}+{16}}}}
x
2
a
+
x
b
+
x
2
+
16
c
x
+
d
where
a
\displaystyle {a}
a
=
b
\displaystyle {b}
b
=
c
\displaystyle {c}
c
=
d
\displaystyle {d}
d
=
Integrating term by term, we obtain that
∫
5
x
3
+
9
x
2
+
64
x
+
96
x
4
+
16
x
2
d
x
=
\displaystyle \int{\frac{{{5}{x}^{{3}}+{9}{x}^{{2}}+{64}{x}+{96}}}{{{x}^{{4}}+{16}{x}^{{2}}}}}{\left.{d}{x}\right.}=
∫
x
4
+
16
x
2
5
x
3
+
9
x
2
+
64
x
+
96
d
x
=
Preview
Question 6 Part 5 of 5
+
C
\displaystyle +{C}
+
C
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\displaystyle
Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity
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