What is the antiderivative of #lnsqrt( 5 x )#? Calculus Techniques of Integration Integration by Parts 1 Answer Lovecraft Jan 9, 2016 #I = (x(ln(5)+ln(x) - 1))/2 + c# Explanation: #I = intln(sqrt(5x))dx# Using log properties #I = 1/2int(ln(5) + ln(x))dx# #I = (xln(5))/2 + 1/2intln(x)dx# For the last integral say #u = ln(x)# so #du = 1/x# and #dv = 1# so #v = x# #I = (xln(5))/2 + 1/2(ln(x)x - intx/xdx)# #I = (x(ln(5)+ln(x) - 1))/2 + c# 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 1453 views around the world You can reuse this answer Creative Commons License