Question

[integrate from 0 to infinity] (ln(x)/x^2

Answer 1

did you try lnx = u ?

Answer 2

yes, it works , only problem is i am stuck in the part plugging in infinity to the equation
\[(1/x)\ln(x)-1/x ] 0 and infinity

Answer 3

\[\large \int\limits_0^{\infty }\dfrac{\ln x }{x^2}~dx = \lim\limits_{a\to 0, b\to \infty} \int\limits_a^b\dfrac{\ln x }{x^2}~dx\]

Answer 4

now its a proper integral,
evaluate it and take the limits

Answer 5

\[\large = \lim\limits_{a\to 0, b\to \infty} \left(\dfrac{\ln a+1}{a} - \dfrac{\ln b +1}{b}\right)\]

Answer 6

right ?

Answer 7

yes thanks