Find me anywhere in the Constitution where it says that Congress' power to declare war must take on a certain and specific form of language. ANYWHERE.
Congress gave the President approval to use military force -- that is more than sufficient. There is no "magic phrase" that makes that any more or less legitimate than a so-called formal declaration of war.
Then why not simply ask for a declaration of war?
I'll tell you why. Because since 1945, both Presidents and Congress have wanted to take the easy way out. Presidents want the complete freedom to act, and Congress doesn't want to take the responsibility to declare war.
If I'm wrong, please correct me. But please include in your response an answer to the above question: If you're going to go to war, why not simply ask for a declaration of war?
Now consider the times the country has gone to war without a formal declaration: Korea, Vietnam, and the two Gulf wars.
Do you see a difference in results between the first set and the second set?