What is the antiderivative of $(x^4)(lnx)$ ?

Question

1788 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-07T21:01:36

$1/5 x^5 ln x - 1/25 x^5 + C$

Note that:

$d/(dx) 1/5 x^5 ln x = x^4 ln x + 1/5 x^5 1/x = x^4 ln x + 1/5 x^4$

$d/(dx) 1/25 x^5 = 1/5 x^4$

So:

$d/(dx) (1/5 x^5 ln x - 1/25 x^5) = x^4 ln x$

So the antiderivative of $x^4 ln x$ is $1/5 x^5 ln x - 1/25 x^5 + C$

What is the antiderivative of (x^4)(lnx)(x^4)(lnx)?