Consider the indefinite integral [8.2³ 18x³ + 7x² + 3x + 4 -dx x¹ + 1x² Then the integrand has partial fractions decomposition a b cx + d + + x² + 1 x² X where a = b = C = d= Integrating term by term, we obtain that 18x³ + 7x² + 3x + 4 dx = x¹ + 1x² +
Consider the indefinite integral [8.2³ 18x³ + 7x² + 3x + 4 -dx x¹ + 1x² Then the integrand has partial fractions decomposition a b cx + d + + x² + 1 x² X where a = b = C = d= Integrating term by term, we obtain that 18x³ + 7x² + 3x + 4 dx = x¹ + 1x² +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the indefinite integral
[82³
[8x³ + 7x² + 3x + 4
-dx
x¹ + 1x²
Then the integrand has partial fractions decomposition
a
b
cx + d
+ +
x² + 1
x² X
where
a =
b =
C =
d
=
Integrating term by term, we obtain that
18x³ + 7x² + 3x + 4
-dx
-
x¹ + 1x²
+C

Transcribed Image Text:Integrate [²²
2 - x + 6
x³ + 3x
-dx.
The partial fraction decomposition is (write all terms as fractions):
dx
The final answer is:
x + 6
[²²
-dx
x³ + 3x
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