I need to integrate

((e^-x)^2 - (-ex)^2)dx

Can someone help?

To integrate the given expression ((e^(-x))^2 - (-ex)^2) dx, we can simplify it first:

((e^(-x))^2 - (-ex)^2) dx
= (e^(-2x) - e^2x) dx

Now, we can integrate term by term:

∫(e^(-2x) - e^2x) dx
= ∫e^(-2x) dx - ∫e^2x dx

For the first part, we can use the rule for integrating e^ax:

∫e^(-2x) dx = -1/2 * e^(-2x)

For the second part, we again use the rule for integrating e^ax:

∫e^2x dx = 1/2 * e^2x

Putting everything together, we get:

∫((e^-x)^2 - (-ex)^2)dx = -1/2 * e^(-2x) - 1/2 * e^2x + C

where C is the constant of integration.