Aren't physics integrals beautiful?

Calculus Level 3

Here's a fun little integral I found a while back. Use your tricks wisely.

exp(ip(xx0))exp(pp0)dp \int _{ -\infty }^{ \infty }{ \quad \exp { \left( \cfrac { ip(x-{ x }_{ 0 }) }{ \hbar } \right) } } \exp \left( -\frac { |p| }{ { p }_{ 0 } } \right) dp

SIMPLIFY AS MUCH AS POSSIBLE, you'll get it wrong if you don't

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