What is the integral of #int xlnx dx #? Calculus Introduction to Integration Definite and indefinite integrals 1 Answer Eddie Jul 3, 2016 #= x^2/2 ln x - x^2/4 + C# Explanation: we use IBP #int u v' = uv - int u' v# #u = ln x, u' = 1/x# #v' = x, v = x^2/2# #= x^2/2 ln x - int dx qquad x/2# #= x^2/2 ln x - x^2/4 + C# 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 83750 views around the world You can reuse this answer Creative Commons License