X*ln(x) = 1/2x^2*ln(x) - 1/4*x^2 not sure how they got it

[mr_coffee]

Hello everyone!

I'm doing a line integral but I'm confused on the integration method used:

I got to integral 1 to 3 2*(x^4+xln(x) ); But they then have:
x^5/5 + 1/2x^2 * ln(x) - 1/4x^2 and I'm not sure how they got the last part, 1/2x^2 * ln(x) - 1/4x^2

Thanks!

u = x isn't what they did I don't think, and its been awhile so I'm rusty on integration XD

 

[Dick]

The 'hard' part is the integral of x*ln(x). And they just integrated by parts.

 

[mr_coffee]

ahh thank you