182k views
1 vote
What is the integral of ln X?

2 Answers

4 votes
Hence, the required integral is ∫ ln x = x ln x - x + C ,where is a constant.
User Davidrynn
by
7.8k points
0 votes

Evaluate,
\int\ {ln(x)} \, dx

Using integration by parts,
uv-\int {v} \, du

Let,
u=ln(x) = > du=(1)/(x)dx

Let,
dv=1dx = > v=x

We now have,


(ln(x))(x)-\int\ {(x)((1)/(x) )} \, dx

=>
xln(x)-\int\ {1} \, dx

=>
xln(x)-x+c

Thus the solution is,
xln(x)-x+c.

User Karl
by
8.1k points