how to get the answer for the following integration?

$ti(t)$ is a function of time which is normally given with (time,value) pairs and not defined mathematically. i need to get the value $td(t)$ by solving the following integration:

$$\int_{t-td(t)}^t\frac{1}{ti(\tau)}d\tau==1$$

so how can I get the values of $td(t)$?

I know that $\int\frac{1}{x}dx = \ln(x)$. Yet, I am not sure how to do it when I only have a numerical values of function $ti(t)$.

Can anyone help me?

thx for the support

-
– Shaun Jul 31 '14 at 10:26
some elaboration is needed – obay Jul 31 '14 at 11:56

To compute the integral you can use, for example, http://en.wikipedia.org/wiki/Trapezoidal_rule. You only need to know the values of the function $ti(t)$ in some points. (the more the better).