Just like:
A=i+j+k
B=2i+3j-4k
They are both vector.
I heard that a vector times a vector become a tensor(rank two).
If ij=-k,ik=-j,jk=-i.
The product is:
(i+j+k)(2i+3j-4k)=-2-3k+4j-2k-3+4i-2j-3i+4=i+2j-5k-1
I think it is still a vector, not a tensor(rank two).
For example
Intergrate (uv dx)=?
Intergrate (u dx/v)=?
Intergrate (u^v dx)=?
Intergrate (log_u v)=?
Where u and v are the function of x.
Is there any method in intergration just like dy/dx=(dy/du)(du/dx) in diffrentiation?