- #1
Denisse
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Homework Statement
How can I integrate this? I already tried substitution u=x-1 and partial fractions.
∫[dx]/[(1-X^2)√((x^2)-3x+2)]
Integrate 1/(x-1)(sqrt(x^2-3x+2))
- Thread starter Denisse
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- Integrate
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SUMMARY
The integral ∫[dx]/[(1-x^2)√((x^2)-3x+2)] can be approached by completing the square within the square root and applying trigonometric substitution. Specifically, the substitution x - 3/2 = 1/2 sec(θ) is recommended for simplification. Users noted the importance of clarifying the integral's expression, as discrepancies exist between the title and the content of the post. Proper identification of the integral is crucial for effective problem-solving.
PREREQUISITES- Understanding of integration techniques, specifically trigonometric substitution.
- Familiarity with completing the square in algebraic expressions.
- Knowledge of the properties of square roots and their manipulation.
- Basic grasp of partial fraction decomposition.
- Study trigonometric substitution methods in calculus.
- Practice completing the square with various polynomial expressions.
- Explore advanced integration techniques, including integration by parts.
- Review the concept of partial fractions and its applications in integration.
Students studying calculus, particularly those tackling integration problems, and educators looking for effective teaching methods in advanced integration techniques.