kill(all);

'integrate(2^x^2,x);

f(x):=2^x^2;

F(x):=''integrate(f(x),x)$ F(x);

F_(x,n):=ratsimp(taylor(F(x),x,0,n))$

F_(x,1); F_(x,3); F_(x,5);F_(x,11);F_(x,21);