JEE Math practice: Indefinite Integral

Calculus Level 4

Let \(f\) be a continuous function satisfying \(f(x+y)=f(x)+f(y)\), for each \(x,y\in\mathbb{R}\) and \(f(1)=2\) then \[\int\frac{f(x)\tan^{-1}x}{(1+x^2)^2}dx\] is equal to

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