Thread: integrating ln(y) w.r.t x

I was looking at the thread where this person list the methods for differential equations. In the exact equation part, he appears to integrate ln(y) with respect to x and obtain xln(y). How do you do this?

Since it is being integrated w.r.t. , is treated as a constant.

What's the integral of a constant?

Originally Posted by Prove It

Since it is being integrated w.r.t. , is treated as a constant.

What's the integral of a constant?

x multiplied by the constant. ahh thanks very much. On a side note, when you differentiate say xy, you do not treat y as a constant. You get y+x(dy/dx). Is that because your treating y as a function of x?

That is implicit differentiation. If y is a function of x, then that is how you would take the derivative.

In this case, you are treating integration as the opposite of PARTIAL differentiation...

Originally Posted by Prove It

In this case, you are treating integration as the opposite of PARTIAL differentiation...

I'm not sure why when you are only dealing with 2 variables, x and y.