What is the antiderivative of #ln(2x)/x^(1/2)#? Calculus Introduction to Integration Integrals of Exponential Functions 1 Answer Eddie Jun 22, 2016 # 2 sqrt{x} ln(2x) -4 sqrt(x) + C# Explanation: IBP using #int u v' = uv - int u' v# #u = ln(2x), u' = 1/x# #v' = x^{-1/2}, v = 2x^{1/2}# #\implies 2 sqrt{x} ln(2x) - int (2 sqrt(x))/x \ dx# #= 2 sqrt{x} ln(2x) - int 2/ sqrt(x) \ dx# #= 2 sqrt{x} ln(2x) - 2 * 2 sqrt(x) + C# #= 2 sqrt{x} ln(2x) -4 sqrt(x) + 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 1120 views around the world You can reuse this answer Creative Commons License