What is the anti-derivative of logex? I know the derviative is 1/x but can't work out the anti-derivative.
Question #58927. Asked by blurrystar1.
Last updated Oct 23 2017.
peasypod
Answer has 5 votes
Currently Best Answer
peasypod 21 year member
3273 replies
Answer has 5 votes.
Currently voted the best answer.
The definite integral of lnx is xlnx - x. (lnx is "log of x to the base e")
Aug 21 2005, 6:11 AM
penguin16
Answer has 4 votes
penguin16
Answer has 4 votes.
That's correct. To work it out, you have to use integration by parts: The integral of u*dv is equal to u*v - (the integral of v*du). This works whenever one part can be diffentiated but not integrated easily, just like lnx. In this case, lnx=u and dx=dv. Then you just plug those values into the formula to solve.
Aug 21 2005, 8:55 AM
tommytippee
Answer has 5 votes
tommytippee
Answer has 5 votes.
if f(x) = xlnx
f'(x) = 1 + lnx (using product rule)
hence (assume antidif is the antidif sign, lil squiggly line wateva)
antidif (d xlnx/dx)dx = antidif(1)dx + antidif(lnx)dx
xlnx - antidif(1)dx = antidif(lnx)dx
xlnx - x + c = antidif(lnx)dx
