How Do You Integrate the Square of dx/dt?

[raisin_raisin]

Hey, not really homework but I am just having a total mind blank and would be grateful if someone could help me.
$$\int\left(\frac{dx}{dt}\right)^{2}dt=?$$
I even have the answer my brain is just refusing to play along though and I just can't picture how to work it out properly at the moment.
Thanks!

 

[rock.freak667]

try writing it as

$$\int \frac{dx}{dt} \frac{dx}{dt} dt$$instead.

 

[raisin_raisin]

try writing it as

$$\int \frac{dx}{dt} \frac{dx}{dt} dt$$


instead.

Thanks for your reply.
In that case I don't have brain freeze I just don't know. I just want to cancel the dt's but then
I get
$$\int \frac{dx}{dt}dx$$
which I don't know how to handle.

 

[Dick]

It's not the sort of an expression where you can eliminate the t dependence. The answer depends on how x depends on t. E.g. if x(t)=t^2, then it's an easy elementary integral, if x(t)=e^(t^2), it's not an elementary integral.