Double integral in Maple involving parameters [closed]

Question

$$\int_{0}^{1}\int_{0}^{1-x}(1-x)(1-y)(x+y)x^{n_1}y^{n_2}(1-x-y)^{n_3}\mathrm{d}y\mathrm{d}x$$

I want to calculate above integral in Maple, the parameters $n_1,n_2,n_3$ are all natural numbers.

I execute the following command:

int(int((1-x)**(1-y)*(x+y)*(x^n_1)*(y^n_2)*(1-x-y)^n_3, y=0..1-x),x=0..1); 

After I pressed enter the following error message appeared:

"Error, unable to match delimiters"

I'm new to Maple, could any one tell me what the problem here is and which would be the correct command? I think I can learn the commands for computing a range of integrals like this once I know the correct command for this integral.

Answer 1

Be careful about the syntax for multiplication. Above your expressions contains,

(1-x)**(1-y)

which is the syntax for powering. Eg, 3**4 evaluates to 81.

Another pitfall of multiplication syntax is to omit a multiplication sign (explicit multiplication) or an appropriately placed space (, for implicit multiplication in 2D Math entry mode). Eg, (1-x)(1-y) would get interpreted as function application.

It's not clear whether you have proper values for n_1, n_2, and n_3. If they are not actual numbers then you may have to place some assumptions (if you know any) on them in order for Maple to get a purely symbolic result. For example, the following leads to symbolic result a few pages long,

int(int( expand( (1-x)*(1-y)*(x+y)*(x^n_1)*(y^n_2)*(1-x-y)^n_3 ),
         y=0..1-x), x=0..1)
            assuming n_1::posint, n_2::posint, n_3::posint; 

You could use nonnegint there instead, if you meant to allow n_1=0, etc.