Effortlessly Integrate \frac{2mdx}{cx^2} from x to 0 | Expert Tips

[Speags]

i need to intergrate this function
$$\frac{2mdx}{cx^2}$$
from x to 0

 

[NateTG]

If you meant to write:
$$\int_x^{0} \frac{2m}{cx^2}dx$$
Then you've got the variable of integration in the limits of integration which is ...problematic.

 

[HallsofIvy]

It is bad practice, although it is often done, to use the same letter to represent the "dummy" variable of integration and as a variable outside the integral (as in one of the limits of integration).

If you meant
$$\int_x^0\frac{2mdt}{ct^2}$$

Then rewrite the t² in the denominator as t^-2:
$$\frac{2m}{c}\int_x^0t^{-2}dt$$

You still have a problem- that's an improper integral which will have serious difficulties at 0! This integral does not exist.