Problem with integral

[Stevetuc]

In this form

Code:

int(e^(-t-i*t),t,(-τ)/2,τ/2)

The result with maximum simplification is:

Code:

((-1+i)*e^((-1-i)*τ/2)+(1-i)*e^((1+i)*τ/2))/2

But if I present the same integral in an expanded form with the real and complex exponents seperated:

Code:

int(e^(-t)*e^((-(i))*t),t,(-τ)/2,τ/2)

I get this result:

Code:

((e^(1/2*τ))^2*(e^(i/2*τ))^2*tan(τ/4)^2+(e^(1/2*τ))^2*(e^(i/2*τ))^2+(-1-i)*(e^(1/2*τ))^2*e^(i/2*τ)*tan(τ/4)^2+(2+2*i)*(e^(1/2*τ))^2*e^(i/2*τ)*tan(τ/4)+(1+i)*(e^(1/2*τ))^2*e^(i/2*τ)+(−i)*(e^(1/2*τ))^2*tan(τ/4)^2+(−i)*(e^(1/2*τ))^2+i*(e^(i/2*τ))^2*tan(τ/4)^2+i*(e^(i/2*τ))^2+(1+i)*e^(i/2*τ)*tan(τ/4)^2+(2+2*i)*e^(i/2*τ)*tan(τ/4)+(-1-i)*e^(i/2*τ)-tan(τ/4)^2-1)/((2+2*i)*e^(1/2*τ)*e^(i/2*τ)*tan(τ/4)^2+(2+2*i)*e^(1/2*τ)*e^(i/2*τ))

It seems like the simplification should be doing a better job with this simple input.

I want to keep the exponents separate because eventually I want to input:

Code:

int(f(t)*e^(-i*t),t,(-τ)/2,τ/2)

Where f(t) is some arbitrary function of t. Obviously f(t) could then be e^(-t) and id prefer it returned the first of the above results!