The following are some examples to be used with Maple. It is possible to "cut and paste" the Maple commands into the Maple program.

Sample syntax:

  1. > int(x^2+5*sin(x),x);

Substitution:

  1. > int(9/sqrt(4-3*x^2),x);

  2. > int(9/(x^2+8*x+25), x);

  3. > int(8*(sec(4*x))^2/(5-3*tan(4*x))^7,x);

Trick:

  1. > int(sec(x),x);

Integration by Parts:

  1. > int(x^7*sin(3*x),x);

  2. > int(exp(-5*x)*cos(4*x),x);

  3. > int(arcsin(x),x);

Reduction Formulas:

  1. > int((tan(x))^11, x);

Partial Fractions:

  1. > int(1/(x^2-4),x);

  2. > int(1/(x^2-1),x);

  3. > int(1/((x-3)^2*(x+5)^3*(x^2+9)^3),x);

Formulas with parameters:

  1. > int(sin(a*x),x);

  2. > int(1/(x^2+a^2),x);

    [Solution.]

  3. > int((b*x+c)/(x^2+a^2),x);

    [Solution.]

Definite Integrals:

  1. > int(sin(x),x=0..Pi);

Functions with non-elementary antiderivatives:

  1. > int(cos(x^3),x);

  2. > int(sin(x^2),x);

Method of Substitution and Maple.

Integration by Parts and Maple.