Can someone please remind me why the antiderivative of ln(x) is xln(x) -x and not 1/x?
B bjackson11 New member Joined Oct 17, 2008 Messages 12 Nov 26, 2008 #1 Can someone please remind me why the antiderivative of ln(x) is xln(x) -x and not 1/x?
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Nov 26, 2008 #2 ∫ln(x)dx\displaystyle \int ln(x)dx∫ln(x)dx If we use parts and let u=ln(x), dv=dx, du=1xdx, v=x\displaystyle u=ln(x), \;\ dv=dx, \;\ du=\frac{1}{x}dx, \;\ v=xu=ln(x), dv=dx, du=x1dx, v=x and put it together, we get xln(x)−x\displaystyle xln(x)-xxln(x)−x I will let you do the actual operations.
∫ln(x)dx\displaystyle \int ln(x)dx∫ln(x)dx If we use parts and let u=ln(x), dv=dx, du=1xdx, v=x\displaystyle u=ln(x), \;\ dv=dx, \;\ du=\frac{1}{x}dx, \;\ v=xu=ln(x), dv=dx, du=x1dx, v=x and put it together, we get xln(x)−x\displaystyle xln(x)-xxln(x)−x I will let you do the actual operations.
D Deleted member 4993 Guest Nov 26, 2008 #3 bjackson11 said: Can someone please remind me why the antiderivative of ln(x) is xln(x) -x and not 1/x When you find the derivative of 1/x - what do you get? -1/x^2 That surely is not "ln(x)" ? Click to expand...
bjackson11 said: Can someone please remind me why the antiderivative of ln(x) is xln(x) -x and not 1/x When you find the derivative of 1/x - what do you get? -1/x^2 That surely is not "ln(x)" ? Click to expand...
