To evaluate the integral \( \int \tan x \tan(x+1) \, dx \), we can use the identity for the tangent of a sum. The identity states that:
\[
\tan(a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}
\]
In our case, let \( a = x \) and \( b = 1 \). Thus, we can write:
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