When computing the Fourier transform of a linear function I get the following result,
\begin{align} \int_{-\infty}^{\infty} dx \ x \ e^{i k x} & = \frac{1}{i k}x \ e^{ikx} \Big|_{-\infty}^{\infty}-\frac{1}{i k} \int_{-\infty}^{\infty} dx \ e^{i k x}\\ & = \lim_{\Lambda \rightarrow \infty} \frac{1}{i k} 2\Lambda \cos(\Lambda k) -\frac{2 \pi }{i k}\delta(k). \end{align}
While the second term is the usual expression appearing in the literature, I am confused about the first one. How do I deal with that term?