What is the value of the integral $\frac{1}{2 \pi \mathrm{i}} \int_{C} \frac{\mathrm{e}^{z}}{z (1-z)^{3}} \mathrm{d} z$? Where $C$ is a positively oriented simple closed curve that does not pass through the points 0 and 1.

Options:
A. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{-1 \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{0 \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{\frac{\mathrm{e}} {4} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{1+\frac{\mathrm{e}} {4} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 \in D \,,}}} \\ \end{cases} \right.
$$
B. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{-\frac{1}{3} \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{1 \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{-\frac{\mathrm{e}} {5} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{1-\frac{\mathrm{e}} {5} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 in D \,,}}} \\ \end{cases} \right.
$$
C. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{-2 \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{2 \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{-\frac{\mathrm{e}} {4} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{2+\frac{\mathrm{e}} {4} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 \in D \,,}}} \\ \end{cases} \right.
$$
D. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{2 \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{-1 \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{\frac{\mathrm{e}} {3} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{2-\frac{\mathrm{e}} {3} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 \in D \,,}}} \\ \end{cases} \right.
$$
E. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{-1 \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{1 \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{\frac{\mathrm{e}} {2} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{1-\frac{\mathrm{e}} {4} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 \in D \,,}}} \\ \end{cases} \right.
$$
F. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{3 \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{0-\frac{1}{2} \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{\frac{\mathrm{e}} {6} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{0+\frac{\mathrm{e}} {6} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 \in D \,,}}} \\ \end{cases} \right.
$$
G. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{\frac{1}{2} \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{1 \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{-\frac{\mathrm{e}} {2} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{1+\frac{\mathrm{e}} {3} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 \in D \,,}}} \\ \end{cases} \right.
$$
H. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{1 \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{-1 \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{\frac{\mathrm{e}} {5} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{0-\frac{\mathrm{e}} {5} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 \in D \,,}}} \\ \end{cases} \right.
$$
I. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{0 \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{1-\frac{\epsilon}{3} \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{-\frac{\mathrm{e}} {2} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{1-\frac{\mathrm{e}} {3} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 \in D \,,}}} \\ \end{cases} \right.
$$
J. $$
\frac{1} {2 \pi i} \int_{c} \frac{\mathrm{e}^{z}} {z ( 1-z )^{3}} \mathrm{d} z=\left\{\begin{cases} {{{0 \,,}}} & {{{when \, \, 0 ∉ D \,, 1 ∉ D \,,}}} \\ {{{1 \,,}}} & {{{when \, \,0\in D\,,1∉D,}}} \\ {{{-\frac{\mathrm{e}} {2} \, \,,}}} & {{{when \, \, 0 ∉ D \,, 1 \in D \,,}}} \\ {{{1-\frac{\mathrm{e}} {2} \, \,,}}} & {{{when \, \, 0 \in D \,, 1 \in D \,,}}} \\ \end{cases} \right.
$$
Answer: J