I know that $ \delta (x) = \frac{1}{2 \pi } \int_{-\infty}^{+\infty} e^{iwx}dw$ and I know indirect methods to solve this.
But I can't solve the integral in a direct way. I tried this site to show me the steps, but it couldn't solve it either.
Can somebody help me to solve this integral in a direct way? $$ \int_{-\infty}^{+\infty} e^{iwx}dw $$ thanks in advance.
P.S: my mean of a direct way: to solve it by solving the integral not saying that: "it is the synthesis equation for the Dirac delta so it is Dirac delta by using the Fourier transform"