Question

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

Answer 1

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

Explanation:

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`