Question

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

Answer 1

So integrate by parts with u = ln x and v' = 1/x^3

Answer 2

is it a natural log?

Answer 3

yahh

Answer 4

then do what james said

Answer 5

I would prefer JamesJ's approach

Answer 6

what have you written? That's not right.

Answer 7

\[ \int uv' = uv - \int u'v \]
with \( u = \ln x, \ v = 1/x^3 \).

Answer 8

@amogh, again, no.

Answer 9

@korcan, I suggest you just try and solve the problem yourself and let us know if you get stuck.

Answer 10

x.O @ amogh

Answer 11

Oh...I'm very sorry! Lost myself. I'll check

Answer 12

OK, I am trying it ,

Answer 13

@korkankonaglu: Don't mind my answer, that's not right

Answer 14

correction to my last math post, u = ln x, v' = 1/x^3. Not v = 1/x^3

Answer 15

ohh k , what was v ?

Answer 16

that's for you to find.

Answer 17

\[ \int uv' = uv - \int u'v \]
with
\[ u = \ln x, \ v' = 1/x^3 \]

Answer 18

v' = dv/dx , if that's interrupting you

Answer 19

here, I think I can use it:
\[\int\limits_{}p(x)logxdx = Q(X)logx - \int\limits_{}\S(x)dx\]

I mean if we take p(x) as x^-3, then we will have : x^-3 * logx * dx

and by using it: we will have :

(-1/(2x^2))logx - (1/(4x^2)) + C

,,,,,,,,,,,,,

\[\int\limits_{}P(x)logxdx ,, u=logx, P(x)dx=dv\]

\[du=(dx)/x, v=\int\limits_{}P(x)dx = Q(x)\]

q(x), is a polnomial of (n+1)degrees.
by these all then we will have :
\[\int\limits_{}P(x)logxdx = Q(x)logx - \int\limits_{}\S(x)dx\]

if I have to give an example:

\[\int\limits_{}x^n logxdx = ? \]
u = logx, x^ndx = dv
du = dx/x , x^((n+1))/ (n+1) = v

then :
\[\int\limits_{}x^n logxdx = (x^{n+1} / (n+1)) - \int\limits_{}(x^n / (n+1))dx\]
and etc....

IS IT RIGHT? :D

Answer 20

Hello guys is it right?

Answer 21

yes, looks right.