The given integral is:
\[
\int \frac{1+\cos \alpha}{\sin \alpha} \, d\alpha
\]
This can be rewritten as:
\[
\int \left( \frac{1}{\sin \alpha} + \frac{\cos \alpha}{\sin \alpha} \right) \, d\alpha
\]
which simplifies to:
\[
\int \csc \alpha \, d\alpha +
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