# Integrating Cosecant

Calculus Level 3

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

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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