How do you find the integral of #int dx/[5x(ln(5x))^2]# from 2 to infinity?

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Answer 1 · 2015-12-07T16:09:44

#1/5int_2^oo1/(xln^2(5x))#

#t = ln(5x)#

if #x = 2# # =># # t = ln(10)#
if #x = oo# #=># # t = oo#

#dt = 1/x#

#1/5int_ln(10)^oo1/t^2dt#

#-1/5[1/t]_ln(10)^oo#

#-1/5(0-1/ln(10))#

#1/(5ln(10))#