Integral of $$$- \frac{1 - t}{t + 1} + \tan{\left(\frac{\operatorname{acsc}{\left(x \right)}}{2} \right)}$$$ with respect to $$$x$$$
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Find $$$\int \left(- \frac{1 - t}{t + 1} + \tan{\left(\frac{\operatorname{acsc}{\left(x \right)}}{2} \right)}\right)\, dx$$$.
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