Question

What is the antiderivative of `lnx`?

Answer 1

`intlnxdx=x(lnx-1)+"c"`

Explanation:

To find an antiderivative of `lnx`, we must find `intlnxdx`. To do so, we use integration by parts.

`intudv=uv-intvdu`

Let `u=lnx rArr du=1/xdx`

And `dv=dx rArr v=x`

So

`intlnxdx=xlnx-intdx=xlnx-x=x(lnx-1)`