How do you integrate #int x^3ln(5x)# by integration by parts method? Calculus Techniques of Integration Integration by Parts 1 Answer Andrea S. Dec 30, 2016 #int x^3ln(5x)dx = x^4/4(ln(5x)-1/4)# Explanation: #int x^3ln(5x)dx = int ln(5x) d(x^4/4) = x^4/4ln(5x) - int x^4/4 d(ln(5x)) = x^4/4ln(5x) - int x^4/4 1/xdx = x^4/4ln(5x)-int x^3/4dx=x^4/4ln(5x)- x^4/16dx=x^4/4(ln(5x)-1/4)# 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 3294 views around the world You can reuse this answer Creative Commons License