To evaluate the integral \(\int \sin(2x) \, d(\tan x)\), we can follow these steps:
### Step 1: Rewrite the integral
We start with the integral:
\[
\int \sin(2x) \, d(\tan x)
\]
We know that the derivative of \(\tan x\) is \(\sec^2 x \, dx\). Therefore, we can rewrite the integral as:
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