Integrating Cosecant

Calculus Level pending

\[ \begin{eqnarray} I_1 &=&\int \csc x \, dx = \int \dfrac{\csc x (\csc x - \cot x)}{\csc x - \cot x} \, dx = \ln | \csc x - \cot x | \\ I_2 &=&\int \csc x \, dx = \int \dfrac{-\csc x (\csc x + \cot x)}{\csc x + \cot x} \, dx = - \ln | \csc x + \cot x | \\ \end{eqnarray} \]

If both calculations above are correct, then \(I_1\) and \(I_2\) differ by a constant. Find \(I_1 -I_2\).

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