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.