Komplex Fourier series

Sketch the periodic function g(t) with period 2 and determine its complex Fourier series when g(t) is given for -1<t<1 by:

$g\left(t\right)=\left\{\begin{array}{l}0 for -1<t<0\\ e^{-t} for 0 \le t <1\end{array}\right.$

Jag har $C_n =\frac{1}{2}{\int }_0^1{e}^{-t}{e}^{in\pi t}dt$ = $\frac{1}{2}\left[-\frac{e^{-(1+în\pi )t}}{(1+in\pi )}\right]\begin{array}{rcl}t& =& 1\\ t& =& 0\end{array}$= $\frac{1}{2}\left[-\frac{e^{-(1+in\pi )}}{(1+in\pi )}+ \frac{1}{(1+in\pi )}\right]$

men sen tar det stopp. Jag antar att de förlänger med konjugatet, dvs (1-i*n*pi) men får inte till uttrycket med rätta tecken.