Integration by parts and simplifying

trajan22
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Hi,
I have been working on this problem for the longest time and have just run in circles with it. I am thinking the answer is obvious but for some reason I am missing it. I need to find \int \frac{ln(x)}{x^2} dx I know that I need to use integration by parts and have tried a number of things, however the only way that the integral seems to be simplified is if I use this set up
u=ln(x) du=1/x
v=? dv=1/(x^2)
but from here I cannot integrate 1/x^2. Am i even on the right track with this one or is there an easier way? someone please help as this problem is truly annoying me.
 
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you're on the right track, but try thinking of 1/x^2 as polynomial, ie: x^(-2).
I'm sure you can integrate that.
 
oh yeah that's right...ok so if i integrate that then its simply -(1/x) correct?
 
trajan22 said:
oh yeah that's right...ok so if i integrate that then its simply -(1/x) correct?

thts correct

(if you are unsure try differentiating (-1/x))
 
oh yeah that's right...I always forget that its really easy to check these types of problems...thanks for all the help
 
I : lnx/x^2 dx
I: (-lnx/x) - I(1/x^2) dx
I: -lnx/x + 1/x + K
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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