## anonymous 5 years ago What is the integral of y/x dx?

1. amistre64

we can change this a bit: dy = (y/x) dx or dy/y = dx/x and integrate (S) both sides. (S) (1/y) dy = (S) (1/x) dx ln(y) = ln(x) + C e^(ln(y)) = e^(ln(x) + C) y=e^(ln(x)) * e^C y=Cx This is my best guess :)

2. anonymous

yes you right

3. amistre64

yay!! :)

4. anonymous

Well…really, $\int\limits(y/x)dx$means to integrate with respect to x, treating everything else as a constant. Thus, $y \int\limits(1/x)=y \ln \left| x \right|+C.$Just sayin'.

5. amistre64

I would love to agree with you carly; but, ... If we undo that we get: d(f(x))/dx = d(y ln(x))/dx f'(x) = y*(1/x)*(dx/dx) + (dydx)*(ln(x)) f'(x) = y/x + y' ln(x). ; which is not the same as (y/x) Right?

6. anonymous

What is the derivative of ln x? Now what's that times a constant y, hmm?

7. amistre64

But the "y" is not a constant; it is an implicit function of "x". If "y" is an independant variable of f(x,y) then yes, we would hold "y" as a constant to find the rate of change of f(x,y) with respect to "x".