Indefinite Integral $\int\frac{1}{1+\tan^{-1}x}\,\text{d}x$

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I tried to solve this indefinite integral, $$\int\frac{1}{1+\tan^{-1}x}\,\text{d}x.$$

I tried taking the change of variable $u=\tan^{-1}x$ but failed to reach a solution.

Can anyone help me?

Thanks in advance.