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(a) Divide the numerator by the denominator to rewrite x^ 3 +4x^ 2 +6x+5 x^ 2 +4 into…
MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals
Problem
(a) Divide the numerator by the denominator to rewrite
x
3
+
4
x
2
+
6
x
+
5
x
2
+
4
\frac{x^{3}+4x^{2}+6x+5}{x^{2}+4}
x
2
+
4
x
3
+
4
x
2
+
6
x
+
5
into a polynomial plus a proper rational term. (b) Decompose the proper rational term into partial fractions. (c) Using the results above, evaluate
∫
x
3
+
4
x
2
+
6
x
+
5
x
2
+
4
d
x
.
\int \frac{x^{3}+4x^{2}+6x+5}{x^{2}+4}\,dx.
∫
x
2
+
4
x
3
+
4
x
2
+
6
x
+
5
d
x
.
Related theory
Division Algorithm for Polynomials
Polynomials
Integration Techniques
Integration by partial fractions
Integrals
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