The techniques used on this page use a special package which must be called by using the following command:

> with(student);

1. 

   > A:=Int(sin(3*x+5),x);

   

   > changevar(3*x+5=u,A,u);

   

   > value(");

   

   > subs(u=3*x+5,");

   

2. 

   > A:=Int(5*x/(1+16*x^4),x);

   

   > changevar(4*x^2=u,A,u);

   

   > value(");

   

   > subs(u=4*x^2,");

   

3. 

   > A:=Int(8*(sec(4*x))^2/(5-3*tan(4*x))^7,x);

   

   > changevar(5-3*tan(4*x)=u,A,u);

   

   > value(");

   

   > subs(u=5-3*tan(4*x),");

   

   Alternative way:

   > changevar(tan(4*x)=u,A,u);

   

   > B:=";

   

   > changevar(-5+3*u=v,B,v);

   

   > value(");

   

   > subs(v=-5+3*u,");

   

   > subs(u=tan(4*x),");

   

4. 

   > A:=Int(5*exp(2*x)/(7+9*exp(2*x)),x=0..3);

   

   > changevar(7+9*exp(2*x)=u,A,u);

   

   > value(");

   

These integrals are solved without using Maple on this page.