What is the integral of lnx?

MathematicalPhysicist

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what is the integral of lnx?
 
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Try writing it as 1*ln(x), then integrate by parts. (Should get x*ln(x)-x).
 

MathematicalPhysicist

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could you show me the entire way?
 
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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

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i got it, thanks.

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

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

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

MathematicalPhysicist

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never mind i found my mistake.
 
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Oops, sorry LQG, I wasn't ignoring you intentionally. Glad you figured it out anyway :smile:
 

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