How do you find the integral of #int dx/[5x(ln(5x))^2]# from 2 to infinity? Calculus Introduction to Integration Definite and indefinite integrals 1 Answer Tom Dec 7, 2015 #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))# Answer link Related questions What is the difference between definite and indefinite integrals? What is the integral of #ln(7x)#? Is f(x)=x^3 the only possible antiderivative of f(x)=3x^2? If not, why not? How do you find the integral of #x^2-6x+5# from the interval [0,3]? What is a double integral? What is an iterated integral? How do you evaluate the integral #1/(sqrt(49-x^2))# from 0 to #7sqrt(3/2)#? How do you integrate #f(x)=intsin(e^t)dt# between 4 to #x^2#? How do you determine the indefinite integrals? How do you integrate #x^2sqrt(x^(4)+5)#? See all questions in Definite and indefinite integrals Impact of this question 1569 views around the world You can reuse this answer Creative Commons License