This is probably very stupid, but today at a lecture, our professor solved a problem where we had to find the time taken to travel from 0-5m, where $v = 3/x$ (velocity is a function of position.)
Then he integrated, $$\int_0^5 x dx = \int_0^t 3 dt$$
The integral of x represents the area under the position time curve which is giving the time taken. How is this possible? Where am I going wrong here?