What is the antiderivative of ln(x)/x? Calculus Introduction to Integration Integrals of Exponential Functions 1 Answer Jim H Apr 1, 2015 #(ln(x))^2/2+C# (Also written #1/2ln^2(x)+c#). Explanation: #ln(x)/x=ln(x)*(1/x)#. The derivative of #lnx# is #1/x#, so #ln(x)*(1/x)# is of the form: #f(x)*f'(x)#, so the antiderivative is #1/2 (f(x))^2 +C#. (Alt notation: #ln(x)/x=ln(x)*(1/x)# is of the form #u (du)/(dx)# whose antiderivative is #u^2/2 +C#.) Answer link Related questions How do you evaluate the integral #inte^(4x) dx#? How do you evaluate the integral #inte^(-x) dx#? How do you evaluate the integral #int3^(x) dx#? How do you evaluate the integral #int3e^(x)-5e^(2x) dx#? How do you evaluate the integral #int10^(-x) dx#? What is the integral of #e^(x^3)#? What is the integral of #e^(0.5x)#? What is the integral of #e^(2x)#? What is the integral of #e^(7x)#? What is the integral of #2e^(2x)#? See all questions in Integrals of Exponential Functions Impact of this question 1732 views around the world You can reuse this answer Creative Commons License