DON'T DO IT!
You can do a great deal of your own research by googleing the danger of labor induction, and encourage you to do so. This is YOUR baby and YOUR body.
The potential of complications do NOT increase exponentially after week 40, but the DO when you induce labor. Dr. Bradley (the pioneer of natural, husband-coached birth) was very vocal about the 11 month pregnancy -- meaning that there is very little definite about the length of pregnancy. Some women carry their babies longer than 40 weeks. As long as there are no signs of stress, the best thing to do is let Mother Nature do what she does best.
The risk of iatrogenic (doctor caused) complications sky rockets when you induce labor -- even if you do it "naturally" by stripping the membranes or drinking a castor oil cocktail. When you induce, your body has not gone through it's own, natural preparations for labor and delivery, so you labor will be longer and much, much more painful.
But worst, your odds of landing in the OR with a c-section - which comes with it's own, separate and very, VERY significant risks (I urge you to google the risks/dangers of c-section).
I went through being forced (for lack of a better term) by doctors to induce. Even though I opted for the least invasive approach of stripping the membranes, after 26+ hours, I was rushed to the OR, where my son was delivered and then taken to the NiCU with a pneumo thorax (a little hole in his lung that often happens to babies delivered by cs), where we stayed for 3 awful days. And a week later I was back in the hospital with an infection in the incision.
Do your own homework, make sure you husband is on board to be your advocate and champion, and then together make YOUR birth plan and stick to it.
Take good care.
Blessings,
M.