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Lee
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Which substituation would I need to use for this intergral;
[y.du/(y^2 + (x - u)^2)]
[y.du/(y^2 + (x - u)^2)]
Substituting for Intergral: Tricky Intergral
- Thread starter Lee
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SUMMARY
The discussion focuses on the substitution method for the integral of the function y.du/(y^2 + (x - u)^2). The integrand resembles the form 1/(1+x^2), which has the antiderivative arctan(x). The recommended substitution involves taking y out of the integral and setting b = x - u, leading to db = -du. This results in the final expression of -tan-1((x-u)/y) as the solution.
PREREQUISITES- Understanding of integral calculus
- Familiarity with substitution methods in integration
- Knowledge of the arctangent function and its properties
- Experience with variable transformations in integrals
- Study advanced techniques in integral calculus
- Learn about variable substitution in definite integrals
- Explore the properties and applications of the arctangent function
- Practice solving integrals involving trigonometric substitutions
Students and professionals in mathematics, particularly those focusing on calculus and integral techniques, as well as educators teaching integration methods.
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