Question

How do you integrate `(x^4)(lnx)`?

Answer 1

`intlnx xxx^4dx=x^5/5(lnx-1/5)`

Explanation:

WE can use integration by parts `intudv=uv-intvdu`

Let `u=lnx` and `v=x^5/5`

Hence `du=dx/x` and `dv=x^4dx` and `intudv=uv=intvdu` is

`intlnx xxx^4dx=intudv=uv-intvdu`

= `x^5/5xxlnx-intx^5/5xxdx/x`

= `(lnx xx x^5)/5-1/5intx^4dx`

= `(lnx xx x^5)/5-x^5/25`

= `x^5/5(lnx-1/5)`