Indefinite integral of polynomial fraction

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Name	Status	Author	Last Modified
Indefinite integral of polynomial fraction	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Luis's copy of Indefinite integral of polynomial fraction	draft	Luis Hernandez	30/11/2018 18:40

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Question statement

Integrate the following function $f(x)$

$f(x)=\simplify[std]{({n}x^3+{m}x^2+{n+p}x +{m})/(1+x^2)}$

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			Name	Type	Generated Value

sp	integer	1
m	integer	5
n	integer	3
p	integer	7
sn	integer	1
sm	integer	1

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xxxxxxxxxx
 
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Description

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Generated value: `integer`

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Parts

Gap-fill
1. Gap Mathematical expression
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$\displaystyle \int f(x)\;dx=\;\;$ Unnamed gap

Input the arbitrary constant of integration as $C$ .

Advice

Since the degree of the numerator of $f(x)$ is greater than the denominator, $f(x)$ is improper.

First, perform a long division, so that $f(x)$ can be rewritten in the form $\displaystyle{f(x)=\simplify[std]{{n}x+{m}+({p}x)/(1+x^2)}}$ .

Each term of this expression can then be integrated using standard functions (to within the arbitrary constant) to give:

$\displaystyle{\int f(x)\;dx=\simplify[std]{{n}x^2/2+{m}x+{p}/2*ln(1+x^2)} +C}$

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Taxonomy: mathcentre

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Indefinite integral of polynomial fraction

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`