How do you integrate ln(sqrt(x)) ? Calculus Techniques of Integration Integration by Parts 1 Answer Eddie Jul 12, 2016 = 1/2 x( ln x - 1) + C Explanation: int \ ln(sqrt(x)) \ dx using IBP: int uv' = uv - int u'v = int \ ln(sqrt(x)) * (x)' \ dx = ln(sqrt(x)) * x - int (ln(sqrt(x)))' * x\ dx = 1/2 x ln x - int \ 1/(sqrt(x)) (1/2 * 1/sqrtx) * x\ dx = 1/2 x ln x - 1/2 int \ dx = 1/2 x ln x - 1/2 x + C = 1/2 x( ln x - 1) + 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 6232 views around the world You can reuse this answer Creative Commons License