How do you evaluate the integral #int (dx)/(x(lnx)^(1/5)# from #1/2# to #oo#? Calculus Introduction to Integration Definite and indefinite integrals 1 Answer Cesareo R. Sep 16, 2016 #int_(1/2)^oo (dx)/(x(lnx)^(1/5)) = oo# Explanation: #int (dx)/(x(lnx)^(1/5)) = 5/4(log_e x)^(4/5)+C# but #log_e x# is a monotonic increasing function with #x# so #int_(1/2)^oo (dx)/(x(lnx)^(1/5)) = oo# 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 1753 views around the world You can reuse this answer Creative Commons License