What is the integral of lnx?

MathematicalPhysicist

Gold Member
what is the integral of lnx?

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Lonewolf

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

MathematicalPhysicist

Gold Member
could you show me the entire way?

Lonewolf

Sure

&int;1*ln(x)dx

du/dx = 1
v = ln(x)

u = x
dv/dx = 1/x

Now, integrating by parts:

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

MathematicalPhysicist

Gold Member
i got it, thanks.

edit: just one problem should this &int;u*dv/dx=&int;1

Last edited:

MathematicalPhysicist

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

edit: just one problem shouldnt this be &int;u*dv/dx=&int;1 ?
lonewolf i think i am wrong but i need your verification on that.

MathematicalPhysicist

Gold Member
never mind i found my mistake.

Lonewolf

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

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