Question

Find the Integral

lnx/3x

Answer 1

\[\int\limits_{}^{}(lnx/3x)dx\]

Answer 2

by parts comes to mind

Answer 3

the 1/3 is a constant so your pretty much left with determining the ln(x)/x portion

Answer 4

So I can make it \[1/3\int\limits_{}^{}lnx/x\]

Would my u be x or lnx?

Answer 5

hmm, u sub

1/x is the derivative of ln(x)

let u = ln(x)
du = dx/x, x du = dx

u*x du
------ = u du
x

Answer 6

So xlnx/x?

Answer 7

no

what is the integral of u du ?

Answer 8

\[let~u=ln(x)\]
\[\frac 13\int u~du\]

Answer 9

\[\frac 13\int\frac 1x~ln(x)~dx\]
\[u = ln(x)~:~du=dx/x\\~~~~~~~~~~~~~~~~ x~du = dx\]
\[\frac 13\int\frac xx~u~du\]
\[\frac 13\int u~du\]

Answer 10

so u^2/2, times 1/3 and we know what u is equal to