Integrating Natural Logarithms: A Scientific Approach

[MathematicalPhysicist]

what is the integral of lnx?

 

[Lonewolf]

Try writing it as 1*ln(x), then integrate by parts. (Should get x*ln(x)-x).

 

[MathematicalPhysicist]

could you show me the entire way?

 

[Lonewolf]

Sure

∫1*ln(x)dx

du/dx = 1
v = ln(x)

u = x
dv/dx = 1/x

Now, integrating by parts:

∫1*ln(x)dx = u*v - ∫u*dv/dx
= x*ln(x) - ∫dx
= x*ln(x) - x (+ C to be pedantic)

 

[MathematicalPhysicist]

i got it, thanks.

edit: just one problem should this ∫u*dv/dx=∫1

 

[MathematicalPhysicist]

Originally posted by loop quantum gravity
i got it, thanks.

edit: just one problem shouldn't this be ∫u*dv/dx=∫1 ?

lonewolf i think i am wrong but i need your verification on that.

 

[MathematicalPhysicist]

never mind i found my mistake.

 

[Lonewolf]

Oops, sorry LQG, I wasn't ignoring you intentionally. Glad you figured it out anyway