Indefinite Integration

$\mathrm{e}^{\sin \theta}\left(\log \sin \theta+\operatorname{cosec}^2 \theta\right)+\mathrm{c}$, (where c is a constant of integration)

$\mathrm{e}^{\sin \theta}(\log \sin \theta+\operatorname{cosec} \theta)+\mathrm{c}$, (where c is a constant of integration)

$\mathrm{e}^{\sin \theta}(\log \sin \theta-\operatorname{cosec} \theta)+\mathrm{c}$, (where c is a constant of integration)

$\mathrm{e}^{\sin \theta}\left(\log \sin \theta-\operatorname{cosec}^2 \theta\right)+\mathrm{c}$, (where c is a constant of integration)