Integration of $\int_\pi^{+\infty}e^{-st}(t-\pi)\,dt$ How can i calculate this integral?
$$
\int_\pi^{+\infty}e^{-st}(t-\pi)\,dt
$$
I tried many different things but i was hopeless.
I know that integrating by parts may be the way to go but i am truly lost.

Integration by parts will give you (choosing $f = t-\pi$ and $g' = e^{-st}$)
$${\displaystyle\int}\left(t-{\pi}\right)\mathrm{e}^{-st}\,\mathrm{d}t=-\dfrac{\left(t-{\pi}\right)\mathrm{e}^{-st}}{s}-{\displaystyle\int}-\dfrac{\mathrm{e}^{-st}}{s}\,\mathrm{d}t +C$$
which is 
$${\displaystyle\int}\left(t-{\pi}\right)\mathrm{e}^{-st}\,\mathrm{d}t=-\dfrac{\left(t-{\pi}\right)\mathrm{e}^{-st}}{s}-\dfrac{\mathrm{e}^{-st}}{s^2} +C$$
Organizing, we get
$${\displaystyle\int}\left(t-{\pi}\right)\mathrm{e}^{-st}\,\mathrm{d}t=-\dfrac{\left(s\left(t-{\pi}\right)+1\right)\mathrm{e}^{-st}}{s^2}+C$$
Evaluating at the boundaries, we get
$${\displaystyle\int_{\pi}^{\infty}}\left(t-{\pi}\right)\mathrm{e}^{-st}\,\mathrm{d}t=\dfrac{\mathrm{e}^{-{\pi}s}}{s^2}$$
