# Question:Maple17 performance on a simple integral of rational function

## Question:Maple17 performance on a simple integral of rational function

Maple 17

Dear all,

I've just discover something quite surprising for me... It turns out like if Maple didn't take in account the linearity of the integral.

In the middle of a calculation, I need to compute the following integral

int(3628800 / (y * (1 / 2 + y)^11) - 3628800 / (y * (39 / 2 + y)^11), y = 39 / 2..infinity);

Maple 17 is not able to instantly answer me, and I'm not so patient... (I've waited more than 30s)

Nevertheless, if I ask Maple 17 to compute

3628800 * int(1 / (y * (1 / 2 + y)^11) - 1 / (y * (39 / 2 + y)^11), y = 39 / 2..infinity);

as well as

int(3628800/(y*(1/2+y)^11), y = 39/2..infinity)-int(3628800/(y*(39/2+y)^11), y = 39/2..infinity);

Maple 17 answer me instantly... which turn out to be quite surprising!

Is there someone, here, who has some ideas of what is happening in this calculation? Why Maple17 has this strange behaviour?