integration of a logarithmic function? (1 Viewer)

[pikto]

i haven't actually managed to find instructions on doing this, that is obviously why i am asking, but if anyone can set me in the right direction then that would be tops!
just a simple one, or a link to a theory/method.

 

[Nobuo Uematsu]

i haven't actually managed to find instructions on doing this, that is obviously why i am asking, but if anyone can set me in the right direction then that would be tops!
just a simple one, or a link to a theory/method.

Use integration by parts.
let u=the log function and dv\dx=1

 

[Antwan23q]

thats if it was Ln but how do u find the derivative of a log function?

 

[yrtherenonames]

A primitive of lnx is x(lnx-1)
The derivative of a log function is 1/x, if you're using base 'e', and if not, use the change of base laws to put it in base 'e'

 

[Antwan23q]

A primitive of lnx is x(lnx-1)
The derivative of a log function is 1/x, if you're using base 'e', and if not, use the change of base laws to put it in base 'e'

i dont follow

 

[withoutaface]

Integrate by parts, like so:
int(lnx dx) = xlnx + int(x * 1/x dx) = xlnx + int(1)dx = xlnx + x + C

 

[Antwan23q]

yeh but how do you do
Int (logx dx)?

 

[Nobuo Uematsu]

yeh but how do you do
Int (logx dx)?

int. ln x dx
let u=lnx and dv\dx=1
du\dx=1\x and v=x
hence int. lnx dx=xlnx-int. x\x dx.......

 

[Antwan23q]

I already know that! im not talk about a log to base e, im talkin about a log to base 10

 

[Nobuo Uematsu]

I already know that! im not talk about a log to base e, im talkin about a log to base 10

"Today 10:04 PM
yrtherenonames A primitive of lnx is x(lnx-1)
The derivative of a log function is 1/x, if you're using base 'e', and if not, use the change of base laws to put it in base 'e'
"

 

[yrtherenonames]

Mate, you know that logx base b=lnx/lnb
Just log laws, so a log of something other than base e is just a constant 1/(lnb) times the log of that in base e

So integral of logx base 10=integral of lnx/ln10
=ln10(integral of lnx)
=x.ln10(lnx-1)

 

[Antwan23q]

yeh thanks for that, why dont you show me then

 

[yrtherenonames]

i just did..is this some kind of joke?

 

[Nobuo Uematsu]

Bring forth an example and we'll try!!

 

[Antwan23q]

ahh i get it now, thanks

 

[Antwan23q]

i was thinkin along the lines of ln x = log x / log e
and got messed up

 

[haboozin]

i was thinkin along the lines of ln x = log x / log e
and got messed up

wouldnt that be

lnx/lne
=
ln x


since log_e e = 1 by definition.

(e to the power of what gives you e -- answer being 1)

 

[yrtherenonames]

Yeh he was doing it backwards, using change of base to change lnx to logx instead of vice versa.

 

[rama_v]

Log x = ln x ...thats the notation thats used (in NSW anyway). Log the the base 10 is just that, its log₁₀x