Question

question attached

Answer 1

using the substitution\[u=\ln e\]find \[\int\limits_{1}^{e}(\ln x)/x .dx\]

Answer 2

I assume that's supposed to be \[u = lnx\]in which case we're using integration by u substitution. We use \[u = lnx\]and find\[du = d(u) = d(lnx) = 1/x * dx\]
Then we substitute these into the equation you have:\[\int\limits_{}^{}\ln(x) * 1/x * dx = \int\limits_{}^{}udu = u^2 / 2 = (lnx)^2 / 2\].
Evaluate this at the endpoints and subtract to find the value of the definite integral.

Answer 3

oops sorry @blacksteel, yes indeed in mean lnx =u hahahahs

Answer 4

when you substituted it in i don't get it could you please expplain thx

Answer 5

oh wait nvm i get it thanks heaps