A question about Fourier transformation
Regarding your integral, it is not quite correct I think. You used partial integration to solve it, which works. Let's consider $\int t {\rm e}^{-\jmath \omega t}{\rm d}t$ and call $f(t) = t$ and $g'(t) = {\rm e}^{-\jmath \omega t}{\rm d}t$ so that $g(t) = -\frac{1}{\jmath \omega}{\rm e}^{-\jmath \omega t}$. Then using $$\int f(t) g'(t){\rm d}t = f(t)g(t)-\int f'(t) g(t) {\rm d}t,$$ we obtain $$\int_0^1 t {\rm e}^{-\jmath \omega t}{\rm d}t = \left[-\frac{t}{\jmath \omega}{\rm e}^{-\jmath \omega t}\right]_0^1 + \frac{1}{\jmath \omega}\int_0^1{\rm e}^{-\jmath \omega t} {\rm d}t.$$ It's close to what you did, but you used $g'(t)$ in the first term instead of $g(t)$.


  ended up finding but still there's e(−ω∗j) stuck which confuses me as i believe the plot should be 2 dimensional only (toward x and ω, not toward j).


Note that $j$ is not a variable! It's the imaginary unit $\sqrt{-1}$. Hence, your expression only depends on one variable, which is $\omega$. Matlab will recognize $j$ as the imaginary unit by default, so you should be all set for plotting it.