Answer to Question #157535 in Calculus for Gourav

Question

Integration[-2xy/(x²+y²)²] with respect to y

Answer 1

$\int \frac{-2xy}{(x^2+y^2)^2}dy=-x\int \frac{1}{(x^2+y^2)^2}d(y^2)=-x \int \frac{1}{(x^2+q)^2}dq$ $=-x\int \frac{1}{w^2}dw=-x(- \frac{1}{w}+constant)$ $=\frac{x}{w}+constant=\frac{x}{x^2+q}+constant$ $=\frac{x}{x^2+y^2}+constant$