Exercises

Follow the instructions for the exercises below

1. When x is less than -2, substitute y= into
   (x should be the result)

   restart
assume(x<-2)
eq1:=1/2*(1+2*y+sqrt(1+4*y-12*y^2))/y
y:=x/(x^2-2*x+4)
eq1
simplify(eq1)

2. Make the appropriate assumption so that the result of is 0.

   restart
assume(n, integer)
eq2:=cos(n*x)
int(eq2, x=0..Pi)

3. When n is real, take the integral with respect to x and simplify:
   

   restart
assume(n, real)
eq3:=((1+x^(1/4))^n)/sqrt(x)
inteq3:=int(eq3, x)
simplify(inteq3)

4. If p is greater than 0, integrate with respect to x from 1 to
   

   restart
assume(p>0)
eq4:=(a*x^2+b*x+c)*exp(-p*x)
inteq4:= int(eq4, x=1..infinity)
simplify(inteq4)