Question

What is the integral of ln X?

Answer 1

Hence, the required integral is ∫ ln x = x ln x - x + C ,where is a constant.

Answer 2

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`.