how to find integration of ln(x) with respect to x, approximation is allowed.

Question

anonymous · Answer

graphical or any kind of logical solution is acceptable....

anonymous · Answer

Use integration by parts..
$$\int\limits \ln(x)dx \rightarrow f=x, F=x, g=\ln(x), g'=\frac{1}{x}$$
$$xln(x)-\int\limits x \frac{1}{x}dx \rightarrow xln(x)-\int\limits dx \rightarrow xln(x)-x+C \rightarrow x[\ln(x)-1]+C$$

anonymous · Answer

thank u very much...

anonymous · Answer

sure thing

anonymous · Answer

but if it is a definite integral problem and x->0. then how would you approach?

anonymous · Answer

sorry made a typo litte f=1

anonymous · Answer

read this link about improper integrals.... it also has examples http://tutorial.math.lamar.edu/Classes/CalcII/ImproperIntegrals.aspx

anonymous · Answer

as far i understood it should go to infinity..