## Very Simple Question, please help: Integral of a derivative squared

Hello,

I am trying to figure out how to integrate this, I know it must be simple but I am not sure how to do it.

$$\int(\frac{dx}{dt})^{2}dt$$

Thanks a lot!
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 I think partial integration can work.
 You just need x defined in terms of t x = x(t) then you can differentiate with respect to t, then you square dx/dt then you integrate that across t from t1 to t2 right?

## Very Simple Question, please help: Integral of a derivative squared

Wait a second is x(t) explicitly known?
 hi, thanks for your answers. x(t) is not known that is why I am not sure how to do it. Otherwise what Nick mentioned would be easily applicable. Any other ideas? What do you mean by partial integration dirk_mec1? Thanks!
 Recognitions: Gold Member Science Advisor Staff Emeritus He means "integration by parts". Do you have any reason to think that there is any simple answer to this question? I can see no reason to assume that $$\right(\frac{dx}{dt}\)^2$$ even has an elementary anti-derivative.
 I dont think you can just integrate $$\int (f'(x))^2 \mbox{d}x$$, right? The integration by parts(thanks hallsofIvy ) however gives: $$x (x'(t))^2 - \int x \cdot 2x' \cdot x''\ \mbox{d}t$$
 I thought that there was an easy equivalence like: $$\int(dx/dt)dt = x$$ I guess not! thanks for your help in any case.