What is the antiderivative of lnx?
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Nov 17, 2006 #2 You can find it by using integration by parts. Let \(\displaystyle \L\\u=lnx; \;\ dv=dx; \;\ du=\frac{1}{x}dx; \;\ v=x\) \(\displaystyle \L\\uv-\int{vdu}\) \(\displaystyle \L\\\int{lnx}dx\) \(\displaystyle \L\\xlnx-\int{x\frac{1}{x}}dx\) \(\displaystyle \L\\xlnx-\int{dx}\) \(\displaystyle \L\\xlnx-x+C\)
You can find it by using integration by parts. Let \(\displaystyle \L\\u=lnx; \;\ dv=dx; \;\ du=\frac{1}{x}dx; \;\ v=x\) \(\displaystyle \L\\uv-\int{vdu}\) \(\displaystyle \L\\\int{lnx}dx\) \(\displaystyle \L\\xlnx-\int{x\frac{1}{x}}dx\) \(\displaystyle \L\\xlnx-\int{dx}\) \(\displaystyle \L\\xlnx-x+C\)
