Substituting for Intergral: Tricky Intergral

[Lee]

Which substituation would I need to use for this intergral;

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

 

[Galileo]

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

 

[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)