How do you find the integral $(x^4)(lnx)$ ?

Question

2100 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-06T07:32:27

$x^3-4/3(x^3) + c$

Integration by parts is
$int utimes (dv) = uv- intv du$

Apply it to this integral:

$int(x^4)(In x) dx$

$u=x^4$
$dv=In x$
SO $v=1/x$

= $x^4times1/x- int1/xtimes4x^3 dx$

= $x^3-4intx^2 dx$

= $x^3-4/3(x^3) + c$

How do you find the integral (x^4)(lnx)(x^4)(lnx)?