Promblem with integration

[Anders]

Yes I used the "closed form" much more loosely defined than Wiki. I was thinking to express the result using named standard functions like erf, erfc, gamma... (these particular once are already implemented in Prime but are nonetheless not in closed form per Wiki).

Anyway, I took another pass at this integration...

You could express int(sin(x^2)x,0,x) only in terms of erf(x) (avoiding erfi(x), S(x) and C(x) altogether). After some complex math you get:

int(sin(x^2),x,0,x) =
(1+i)*√(pi/32)*( erf( (1+i)/√(2) * x) - i*erf( (1-i)/√(2) * x) )

So int(sin(x^2)x,0,8) =
(1+i)*√(pi/32)*( erf( (1+i)/√(2) * 8.0) - i*erf( (1-i)/√(2) * 8.0))
should come out as 0.601721644935

   
Not sure if it's enough closed form though.