Substituting for Intergral: Tricky Intergral

Thread starter Lee
Start date Nov 12, 2006

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To solve the integral involving y.du/(y^2 + (x - u)^2), a substitution is needed to simplify the integrand. The integrand resembles 1/(1+x^2), which has an antiderivative of arctan(x). By taking y out of the integral and substituting b = x - u, with db = -du, the expression can be transformed. This leads to the result of -tan^(-1)((x-u)/y) as the antiderivative. The discussion emphasizes the importance of appropriate substitutions to match known integral forms.

Nov 12, 2006

Lee

Which substituation would I need to use for this intergral;

[y.du/(y^2 + (x - u)^2)]

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Nov 12, 2006

Galileo

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The integrand looks like 1/(1+x^2) which has antiderivative arctan(x). Try to make substitutions to match that expression.

Nov 13, 2006

Lee

Got it, take the y out the intergral, make b=x-u then db=-du sub in and use the arctan intergral, getting -tan^-1((x-u)/y)

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