I have a problem in signals and systems to solve which is basically math
So suppose we have two functions x(t) = H(t) which is the Heaviside unit step function as input and an impulse response
$$h(t)=e^{-\left | t \right |} + e^{-\left | 2t \right |}$$
which is $$h(t)=(e^t+e^{2t})H(-t)+(e^{-t}+e^{-2t})H()t)$$
We want to calculate the convolution between them.
At a point i have reached this integral
$$\int_{-\infty }^{\infty }(e^\tau + e^{2\tau })H(-\tau )H(t-\tau )d\tau $$
I think it is zero but I cannot explain why this is true
Any help is welcome