# Lab sheet 7

Exercise 1

y:integrate(((x^3+1)/(x^2+1))^3,x)$

wxplot2d([y,x^4/4],[x,1,10],[legend,"y","x^4/4"]);

kill(y)$

Exercise 2

assume(c>0)$ assume(d>0)$

y: integrate((a*x^2+b)/(c*x^2+d),x);

limit(y/x,x,inf);

Exercise 3

integrate(x/(x^2+1),x);

Exercise 4

b:random(11)-5$ c:random(11)-5$ 
y: x^2+b*x+c; Δ:b^2-4*c;I:integrate(1/y,x);
wxplot2d(y,[x,-10,10],[box,false],[axes,solid]);

Exercise 5: omitted

Exercise 6: omitted