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The answer to the integral would be x((ln(x))^2-2ln(x)+2) It's not a very fun integral :P
i got that from wolfram too but i need to know how
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.
chain rule is from differentiating..the techniques i know are u sub, by parts, trig id, partial fraction...
i know integrating lnx gives xlnx-x+C
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 :(
well x*all those, but you get my point ha
ok, just like idk why lnx is xlnx-x+C...fair enough
o wait, cuz of int by parts...
ln(x) is x*(ln(x)-1) because it's the negative number of whatever the most recent ln is.
o it was by parts the whole time...got it
yes, by parts u=(lnx)^2 dv=1