a. (2+x)2
F(x) = ∫(2+x)2dx; //Subs.: t=2+x, dx=dt
F(x) = ∫t2dt;
F(x) = 1/3*t^3 +c = 1/3*(2+x)^3 +c;
b. (2+x)3
F(x) = ∫(2+x)3dx; //Subs.: t=2+x, dx=dt
F(x) = ∫t3dt;
F(x) = 1/4*t^4 +c = 1/4*(2+x)^4 +c;
c. (x-1/x2)
F(x) = ∫ x dx - ∫ x^{-2} dx;
F(x) = 1/2*x^2 - 1/(-2 +1)*x^{-2+1} +c;
F(x) = 1/2*x^2 +1/x +c;