Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent

integral from three to infinity of ln(x)/x

it is divergent....................................................................................................

why?

when we evaluate the limit it becomes infinity......

so this is divergent.....................

Very sorry my friend, I am terrible in math, so I was wondering if you could posting how you got there? (steps)

ok...

∫ [ ln(x) / x ] dx for x = 3 to x = + infinity Use substitution u = ln(x), then du = (1/x) dx, and the integral is ∫ u du = [ u^2 / 2 ] + C

= [ ln^2(x) /2 ] + C.

To check for converges, you have to do the indefinite integral from x = 3 to x = + infinity limit -> + infinity [ ln^2(x) / 2 ] when x at t = + infinity and t = 3 = + infinity.

so it is divergent.......................................................

hope you understood........thank you

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