How Do You Solve ∫ln(x)dx?

[KSCphysics]

One of my recent problems is with double integrals... and I am having a brain fart on the $$\int ln(u) du$$ can you do this?

 

[NateTG]

You can do it by parts. Consider that
$$\frac{d}{dx} x \ln x = \ln x + 1$$

 

[KSCphysics]

hrmm... i see what your saying..

 

[iluvsr20s]

wouldn't it just be 1/u?
unless that little dash is a negative sign mean your are integrating 1/ln(u) then I'm not sure but i think it would just be u then, but i am probably wrong

 

[ahrkron]

iluvsr20s,

You are probably confused with the fact that $$\int \frac{1}{u} du = \ln x + c$$. It is not the other way around.

 

[philosophking]

Pfft...

... hehe. this ain't too bad. Can we change it to int(ln(x),dx) though? It's how I've always done it notation-wise.

let u = ln(x), dv = dx --> du = 1/x(dx), v = x

So, u*v -int(v,du) = int(u,dv)

x*ln(x) - int(1,dx) = int(ln(x),dx)
x*ln(x) - x = int(ln(x),dx)

Et voila.