How integrate ∫ y^(x) dy

[mr_anderson]

Hi
I was wondering how would I integrate Y to the power x over dy

∫ y^(x) dy

knowing that both x and y are variables, let us. Can I treat X as a constant in this integration or what?
Regards.
Anderson.

 

[_Eduardo_]

Integrate by parts
∫ y^x dy = y y^x - x ∫ y y^(x-1) dy = y^(x+1) - x∫ y^x dy
∫ y^x dy + x∫ y^x dy = (1+x)∫ y^x dy = y^(x+1)

--> ∫ y^x dy = y^(x+1)/(x+1)

Or... try WolframAlpha ;-)

 

[mr_anderson]

Thank you very much
So can't I just consider the x to be just like any other constant since I am integrating in terms of Y because the final result of the integration shows that X behaves just like any other constant, is this right or I am missing something here?
Regards.
Anderson

 

[lostinxlation]

you can, just like a double integration of f(x)g over dx and dy.

 

[embedsys]

If you are going to integrate just ∫ y^(x) dy wrt y. then you can consider x as constant. directly you can get y^(x+1)/(x+1). but if LHS is having some variable functions. then you should follow _Eduardo_ (i.e integrate by parts method).

 

[mr_anderson]

Well thank you guys very much.
the LHS is just f(x)= ∫ y^(x) dy
So I think I can integrate over y and consider x as a constant as you said.
Thank you again.