Maple worksheets on integration techniques |

Basic calculus topics:

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Changing variables in integrals-changevar.mws

- Using the Maple procedure
changevar.- Miscellaneous substitutions.
- Integrals of even and odd powers of sine and cosine.

Inverse Trigonometric Functions-invtrig.mws

- The arcsine function.
- The arccosine function.
- The arctangent function.
- A definite integral involving arctan.
- A definite integral involving arcsin.
- Standard integrals involving inverse trig functions.
- The area under a semicircle.

Integration of rational functions using partial fractions .. I-parfrac1.mws

- Area under the graph y=1/x.
- Introduction to the integration of rational functions.
- Examples of integrals involving partial fraction expansions with distinct linear factors in the denominator.
- The integral of the rational form f '(x)/f(x).
- More examples of integrals of rational functions.
- The integral with respect to x of 1/(a x + b) is ln(|a x + b|)/a +c .. examples
- Partial fractions expansions for the case of repeated linear factors in the denominator.
- Partial fractions expansions for the case of repeated quadratic factors in the denominator.
- Degree of numerator greater than or equal to degree of the denominator.

Integration of rational functions using partial fractions .. II-parfrac2.mws

- More integration examples involving partial fractions.

Integration of rational functions using partial fractions .. III-parfrac3.mws

- Partial fractions expansions for the case of repeated linear factors in the denominator.
- The integral with respect to x of (p x + q)/(a x^2 + b x + c).
- Partial fraction expansions which involve irreducible factors in the denominator.
- Degree of numerator greater than or equal to degree of the denominator.

Integration of rational functions using partial fractions .. IV-parfrac4.mws

- The integral with respect to x of 1/(x^2+a^2)^n.
- Partial fractions expansions which involve repeated irreducible quadratic factors in the denominator.

Integration of rational functions using partial fractions .. V-parfrac5.mws

- The integral with respect to x of 1/(x^3+1).
- The integral with respect to x of 1/(x^4+1).
- The integral with respect to x of 1/(x^5+1).

Integration by parts-intparts.mws

- The integration by parts formula.
- A procedure for performing integration by parts:
intbyparts.- Examples.