Indefinite Integration

$-\mathrm{e}^x \cot \frac{x}{2}+\mathrm{c}$,(where c is a constant of integration)

$\mathrm{e}^x \cot \frac{x}{2}+\mathrm{c}$, (where c is a constant of integration)

$\mathrm{e}^x \operatorname{cosec} \frac{x}{2}+\mathrm{c}$,(where c is a constant of integration)

$-\mathrm{e}^x \operatorname{cosec} \frac{x}{2}+\mathrm{c}$, (where c is a constant of integration)