Section 4.5 Examples
Calculus I
Andy Long

(* #2, p. 335: *)
Integrate[x^3*(2+x^4)^5,x]

(* #5, p. 335 *)
Integrate[Cos[x]^3 Sin[x], x]

(* #8, p. 336 *)
Integrate[x^2 Cos[x^3], x]

(* #19, p. 336 *)
Integrate[(x^2+1)(x^3+3x)^4, x]

(* #38, p. 336 -- the two integrals are equal, so the areas are equal! *)
Plot[x Cos[x^2], {x,0,Sqrt[Pi]}]
Plot[Cos[u]/2, {u,0,Pi}]
Integrate[x Cos[x^2], {x,0,Sqrt[Pi]}]