Problem:
Using Maple, evaluate the following integrals by the method of substitution:


Solution:

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.