r:integrate(sin(a*x^3)/x,x);
=>
-(%i*gamma_incomplete(0,%i*a*x^3)-%i*gamma_incomplete(0,-%i*a*x^3))/6
What is gamma_incomplete(0,z) where z in C ?
limit(r,x,inf);
=>
0
This is wrong.
limit(gamma_incomplete(0,-%i*t),t,inf);
=>
gamma_incomplete(0,infinity)
Wrong, because gamma_incomplete(0,infinity) not exists. This problem entails
limit(gamma_incomplete(0,%i*t),t,inf)-limit(gamma_incomplete(0,-%i*t),t,inf);
=>
0
02.06.2012 0:39, ?????? ??????? ?????:
> integrate(sin(a*x^3)/x, x, 0, +inf);
> maxima result: 0;
> correct result: %pi * abs(a) / 6 / a;