Integration using Partial Fractions (AQA A-Level Mathematics): Flashcards

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Integration using Partial Fractions
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Integration method for rational functions

Integration using partial fractions

1st step: partial fraction integration

Factor the denominator

2nd step: partial fraction integration

Express as sum of partial fractions

3rd step: partial fraction integration

Solve for constants

4th step: partial fraction integration

Integrate each term separately

Partial fraction form for x2+ax^2 + a denominator

rac{Ax + B}{x^2 + a}

Methods to find partial fraction constants

Substitute values or equate coefficients

int rac{1}{x+a} dx

ln∣x+a∣+cln|x+a| + c

ln∣a∣−ln∣b∣ln|a| - ln|b| simplified

ln| rac{a}{b}|

When numerator degree geqgeq denominator degree

Perform polynomial division first

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Integration

Further Integration

Differential Equations

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Integration

Further Integration

Differential Equations

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Integration

Further Integration

Differential Equations

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Integration

Further Integration

Differential Equations

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