Originally posted by absol:
hi, how to integrate (ln x)/x?
is this method in a level syllabus..and what is its name? i only noe the first step can do integration by parts...thx for helping..
integration by parts alone can solve the question
By Parts:
Integrate u dv/dx = uv - Integrate v du/dx (my usage might be slightly different; it is the concept that counts)
if you see, ln x is hard to integrate, so we let u = ln x
dv/dx = 1/x
du/dx = 1/x
v = ln x
Hence, (I{x} = Integrate x)
I{(ln x)/x} = (ln x)^2 - I{(ln x)/x}
2 * I{(ln x)/x} = (ln x)^2
I{(ln x)/x} = (ln x)^2 / 2 + cTo check, differentiate right hand side
You get (ln x) / x, which means the integration was done correctly