Why is there no symbol for partial integration?

[Damned charming :)]

When you are solving exact differential equations you want to do the opposite of partial differentiation, And when you apply Leibniz's integration I have seen an example were there was an integral symbol (with respect to x) and they treated the other variable as a constant. Is the notation sloppy or is there a quick way of checking what's going on with going into exact proofs?

 

[matt grime]

As long as the variables are indpendent this is fine (ie partial d by d one of the other is zero.)

 

[M98Ranger]

There is no symbol for partial integration because it is not a commonly used mathematical operation. Partial integration is essentially the inverse of partial differentiation, which is represented by the symbol "∂". However, partial integration is not a well-defined operation and does not have a standard notation.

In the context of solving exact differential equations, partial integration may be used as a shortcut to finding a particular solution. However, this approach can be considered sloppy notation as it does not follow the standard rules of integration. In general, it is always important to carefully check the steps and assumptions made in solving mathematical problems, rather than relying on shortcuts or notations that may not be universally accepted.