If
\[
\int \frac{\tan x}{1+\tan x+\tan^2x}\,dx
=
x-\frac{K}{\sqrt A}
\tan^{-1}
\left(
\frac{K\tan x+1}{\sqrt A}
\right)
+C,
\]
then the ordered pair \((K,A)\) is
Show Hint
For integrals involving \(\tan x\), use \(t=\tan x\). After converting to a rational function, complete the square in the denominator to obtain inverse tangent terms.