How do you integrate #int x^2lnabs(x)# by integration by parts method? Calculus Techniques of Integration Integration by Parts 1 Answer Martin C. Feb 2, 2018 #1/9x^3(3ln(x)-1)# Explanation: Integration by parts: #int(v'*u)=u*v-int(v*u')# Let #u=ln(x), u'=1/x# and #v'=x^2,v=1/3x^3# #int(x^2ln(x))# #=1/3x^3ln(x)-int(1/3x^(cancel(3) 2)*1/cancel(x)# #=1/3x^3ln(x)-1/9x^3# #=1/9x^3(3ln(x)-1)# Answer link Related questions How do I find the integral #int(x*ln(x))dx# ? How do I find the integral #int(cos(x)/e^x)dx# ? How do I find the integral #int(x*cos(5x))dx# ? How do I find the integral #int(x*e^-x)dx# ? How do I find the integral #int(x^2*sin(pix))dx# ? How do I find the integral #intln(2x+1)dx# ? How do I find the integral #intsin^-1(x)dx# ? How do I find the integral #intarctan(4x)dx# ? How do I find the integral #intx^5*ln(x)dx# ? How do I find the integral #intx*2^xdx# ? See all questions in Integration by Parts Impact of this question 1515 views around the world You can reuse this answer Creative Commons License