10 points to whoever can explain this clearly?

Question

Could someone please explain to me how the following expression equals 0? I've done it out, but I'm having trouble seeing why.

1/2 ∫ x*e^(px) dx + 1/2 ∫x*e^(-px) dx

Here, the limits on the first integral go from negative infinity to 0 and the limits on the second integral go from 0 to infinity.

Answer 1

The two integrals are symmetric around the origin. Compare the values of the expressions under the integrals at -x for the left one and x for the right one. At every point, one will be the negative of the other.

Answer 2

its goes back to basic multiplication any number x 0 is automatically o