Integral

• Jan 20th 2010, 05:17 PM
tylerl
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,
• Jan 20th 2010, 06:04 PM
Freezingbeast
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.
• Jan 20th 2010, 06:12 PM
tylerl
If that were the case then wouldn't it be just...

$\displaystyle y*y^ln(y)-\int 0*y dy$

which would just be y*y^ln(y)?
• Jan 20th 2010, 06:15 PM
Abu-Khalil
Im not sure, but I believe that function does not have a primitive.
• Jan 20th 2010, 06:26 PM
tylerl
So what might you suggest I do to solve this?
• Jan 20th 2010, 09:29 PM
Freezingbeast
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.