Calculate the following integral:
$$\int_{-\infty}^{+\infty}e^{itx-2|x|} \ dx $$
2026-03-27 15:35:53.1774625753
How to do this integration
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Often when you have an absolute value, you can divide into cases. Here, you could write $$ \int_{-\infty} e^{itx-2|x|}\,dx=\int_{-\infty}^0e^{itx+2x}\,dx+\int_0^{+\infty}e^{itx-2x}\,dx. $$ Then you just find a primitive function and insert limits.