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but he's first starting with the case where n=1

Then while using integration by parts he gets this integral for [itex]\int{vdu}[/itex] [tex]2 \int{\frac{x^2}{(x^2+1)^2}dx}[/tex]

then he writes x^2=x^2+1-1 and gets [tex]\int{\frac{1}{x^2+1}dx}-\int{\frac{1}{(x^2+1)^2}dx}[/tex]

now I dont understand why he gets those two integrals as a result of writing x^2 as x^2+1-1, can anybody please help me out here?