evaluate the integral

integral of (ln(4x))^2dx

Question

evaluate the integral

integral of (ln(4x))^2dx

anonymous · Answer

im assuming this is integration by parts. but i am not sure what to make my u and what to make dv

anonymous · Answer

would ln(4x) be good for u? and i would use chain rule to find derivative?

astrophysics · Answer

$$\int\limits (\ln(4x))^2 dx$$ is it like this?

anonymous · Answer

yes it is

astrophysics · Answer

You can just let u = (ln(4x))^2 and dv = 1

anonymous · Answer

hey astrophysics can you please help me I posted a question

anonymous · Answer

ok! where do you get the 1 from?

anonymous · Answer

pls help i need to get rest

astrophysics · Answer

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 · Answer

I guess it would've been better if I said dv = 1*dx

anonymous · Answer

ohh yes i see! thank you

anonymous · Answer

astro pls help

astrophysics · Answer

Not tanx I meant arctanx haha

anonymous · Answer

hmm im not getting the right answer..  is it correct to say that the integral of ln4 is = to xln4 ?

anonymous · Answer

$$(\ln(4x))^{2}x-\int\limits x \frac{ 2\ln4 }{ x } dx$$

anonymous · Answer

so then i cancel out the x on the outside and the x in the denominator..

anonymous · Answer

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 · Answer

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 · Answer

$$(\ln(4x))^2x-2xln4$$ that is my answer..

anonymous · Answer

but the answer says incorrect..

imqwerty · Answer

the answer is $$x(\ln (4x))^2-2xln (4x)+2x$$   recheck once again :)

jhannybean · Answer

You're almost there.

anonymous · Answer

thank you.. i am not seeing where the 2x at the end comes from.. ?

anonymous · Answer

attachment

anonymous · Answer

that is my work so far

imqwerty · Answer

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 · Answer

ok i see, thank you!

imqwerty · Answer

no prblm but that is a long method..