You can use both. I think the infinitive is used more often, maybe the accusative when it is more specific. I dont know. I just know you can use both

Well I´m confused now  because both in my Turkish learning book and in the course I had last winter we were told that istemek always took the infinitive .  And in post 14 of this thread:

http://www.turkishclass.com/forumTitle_1729_2  cyrano makes the point that this is ´better´.  But since you are studying Turkish DK I can hardly disagree with you!  Why is learning Turkish SO confusing???

 It can be better or preferable, but grammatically using accusative is not wrong. And saying that ´istemek always takes infinitive´ is a wrong statement. Let´s make it aorist past time:

Ben polis olmayı çok isterdim

- I wanted to become a cop so much (I would have liked, but I didnt become). Using the infinitive here is wrong.

I think it is only with the şimdiki zamanı that you can use both, though I think infinitive would be preferable.  But in past time, you cannot use infinitive.

Both are correct but I thought some and I realized this difference:

When you say "yapmayı istiyorum" it express wish of the activiy "yapmak" (to do)

It means "I want something but the important thing is that to do (something)" or "What I want is to do (something)"

When you say "yapmak istiyorum" it doesn´t express something, it just says what the wish is.

It means "I want to do (something)", some easier idea...

***

If you want to express the time or the quality or the amount of your want, then you should use that expressed word just before the predicate (verb) and it makes the activity change as -mayı form:

Türkçe öğrenmek istiyorum

but;

• activity expressed (What?)
  

Türkçe öğrenmeyi istiyorum (What I want is to learn Turkish)

• time expressed (When?):

 Türkçe öğrenmeyi yarın istiyorum (I want tomorrow)

• quality/the style (How?):

Türkçe öğrenmeyi seninle istiyorum (I want it with you)

• amount expresed (How much?):

Türkçe öğrenmeyi çok istiyorum (I want much)

Thanks That was a clear explanation!