anonymous
  • anonymous
evaluate the integral integral of (ln(4x))^2dx
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
im assuming this is integration by parts. but i am not sure what to make my u and what to make dv
anonymous
  • anonymous
would ln(4x) be good for u? and i would use chain rule to find derivative?
Astrophysics
  • Astrophysics
\[\int\limits (\ln(4x))^2 dx\] is it like this?

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anonymous
  • anonymous
yes it is
Astrophysics
  • Astrophysics
You can just let u = (ln(4x))^2 and dv = 1
anonymous
  • anonymous
hey astrophysics can you please help me I posted a question
anonymous
  • anonymous
ok! where do you get the 1 from?
anonymous
  • anonymous
pls help i need to get rest
Astrophysics
  • Astrophysics
We can think of there being a 1 when we have such functions dv=dx, it's like if you have to integrate tanx dx you would use by parts, lets u = tanx, and dv = dx
Astrophysics
  • Astrophysics
I guess it would've been better if I said dv = 1*dx
anonymous
  • anonymous
ohh yes i see! thank you
anonymous
  • anonymous
astro pls help
Astrophysics
  • Astrophysics
Not tanx I meant arctanx haha
anonymous
  • anonymous
hmm im not getting the right answer.. is it correct to say that the integral of ln4 is = to xln4 ?
anonymous
  • anonymous
\[(\ln(4x))^{2}x-\int\limits x \frac{ 2\ln4 }{ x } dx\]
anonymous
  • anonymous
so then i cancel out the x on the outside and the x in the denominator..
anonymous
  • anonymous
and i am left with the integral of 2ln4, so then i take out the 2 and put it behind the integral, and i am left with the integral of ln4
anonymous
  • anonymous
from there i took the integral of ln4 which i believe is xln4 and i put both parts together but the answer is incorrect
anonymous
  • anonymous
\[(\ln(4x))^2x-2xln4\] that is my answer..
anonymous
  • anonymous
but the answer says incorrect..
imqwerty
  • imqwerty
the answer is \[x(\ln (4x))^2-2xln (4x)+2x\] recheck once again :)
Jhannybean
  • Jhannybean
You're almost there.
anonymous
  • anonymous
thank you.. i am not seeing where the 2x at the end comes from.. ?
anonymous
  • anonymous
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anonymous
  • anonymous
that is my work so far
imqwerty
  • imqwerty
u=4x \[\int\limits\frac{ (\ln (u)) }{ 4}du \]after some vry bad calculations nd simplifications u get- \[\frac{ 1 }{ 4 }((u)(\ln (u))^2 -2\ln (u)+2(u))\]and then when u simplify nd put u=4x then u get that answer..
anonymous
  • anonymous
ok i see, thank you!
imqwerty
  • imqwerty
no prblm but that is a long method..

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