Question

Please can I get an answer to the integral of in(x)? Thanks

Answer 1

`I=x(ln(x-1))+C`

Explanation:

Assuming we want to solve

`I=intln(x)dx`

Use integration by parts

`color(blue)(intudv=uv-intvdu)`

Let `u=ln(x)` and `dv=1dx`

Then `du=1/xdx` and `v=x`

`I=ln(x)x-intx1/xdx`

`=ln(x)x-intdx`

`=ln(x)x-x+C`

`=x(ln(x)-1)+C`