Trying to find a symbolic solution to an integral with Integrate
:
Integrate[SinIntegral[x^11]/x^(7), {x, 0, Infinity}]
The solution found is:
-(11/72) (-1)^(5/22) (-1 + (-1)^(6/11)) Gamma[5/11]
The numerical value is computed by typing:
-(11/72) (-1)^(5/22) (-1 + (-1)^(6/11)) Gamma[5/11] // N
The numerical result is:
0.449925 -8.32667*10^-17 I
Another way of coding:
Limit[Integrate[SinIntegral[x^11]/x^(7), {x, 0, a}], a -> Infinity]
The result here is:
(Sqrt[\[Pi]] Gamma[5/22])/(12 2^(6/11) Gamma[14/11])
The numerical result here is:
0.449925
I could assume that the complex result is nearly equal to zero, and the two results found are equal.
But when I use NIntegrate
and type
NIntegrate[SinIntegral[x^11]/x^(7), {x, 0, Infinity}]
The value yielded is
0.197976
The numerical value with NIntegrate
is given without error notifications and is the same for increasing WorkingPrecision
.
Why the different numerical results between Integrate
and NIntegrate
?