how do you integrate (lnx)^2?

Question

anonymous · Answer

$$\int\limits_{?}^{?} (lnx)^{2}dx$$

anonymous · Answer

The answer to the integral would be x((ln(x))^2-2ln(x)+2) It's not a very fun integral :P

anonymous · Answer

i got that from wolfram too but i need to know how

anonymous · Answer

I think you treat it like chain rule...? Soo this integral is x(ln(x)^2-2ln(x)+2)

and if it were the integral of ln(x)^3 it would be x(ln(x)^3-3ln(x)^2+6ln(x)-6) and so on and so forth.

anonymous · Answer

chain rule is from differentiating..the techniques i know are u sub, by parts, trig id, partial fraction...

anonymous · Answer

i know integrating lnx gives xlnx-x+C

anonymous · Answer

I have no idea how to explain it then xD I just know it. This is one thing i'm just not sure on how to explain. it's just ln(x)-1, ln(x)^2-2ln(x)+2, etc. It's just how i've known it. i guess it's never really been explained to me, its just how it is. Sorry i couldn't be of help :(

anonymous · Answer

well x*all those, but you get my point ha

anonymous · Answer

ok, just like idk why lnx is xlnx-x+C...fair enough

anonymous · Answer

o wait, cuz of int by parts...

anonymous · Answer

ln(x) is x*(ln(x)-1) because it's the negative number of whatever the most recent ln is.

anonymous · Answer

o it was by parts the whole time...got it

turingtest · Answer

yes, by parts
u=(lnx)^2
dv=1