Thread: Integral

y^ln(y)

I have trying to solve this Integral for quite some time and since I have not really been taught very well, I am having a hard time. The section is on solving integrals by parts but I really cannot tell which would be u and which would be v'.

I would not like anyone to do the problem for me, just looking for something to spark my brain (although the spark might need to be quite big).

Thanks you and sorry for the impending stupidity,

Ty Larson,

Its always really helpful to write out the intergral in proper notation, which will give you a dy at the end

now you can just set dv to dy, and i believe the derivative of y^ln(y) is just 0 (y^lny is a constant), correct me if i'm wrong.
so u=y^ln(y)
du=0
dv=dy
v=y

I believe by parts shouldn't be that hard after that.

If that were the case then wouldn't it be just...



which would just be y*y^ln(y)?

Im not sure, but I believe that function does not have a primitive.

So what might you suggest I do to solve this?

you were doing it right... the answer i believe is y*y^lny+C

if you take the derivative of that, you would arrive with what you had before.