Integration Techniques

Integration Techniques

No silver bullet. Here is the review of basic integration techniques, together with some of the challenging problems presented at University of North Texas Integration Bee. You will see that even computer algebra systems such as Maple and Mathematica are not tough enough to complete them. Nevertheless, you could outperform smart software with the basic techniques we have learned.

Derivatives and integrals of basic functions.

 Functions Derivatives Indefinite integrals Fundamental theorem of calculus Power and logarithmic functions () Exponential functions Trigonometric functions Hyperbolic functions Inverse trigonometric functions Inverse hyperbolic functions

Formulas and identities of basic functions.

 Logarithmic and Exponential functions Trigonometric functions where and . Hyperbolic functions

You may find them useful in the following half-angle tangent'' substitution:

 Substitution Identities , ; , , .

Strategy for integration with sample problems.

A. Substitution rules.

(A.1).

(A.2).

(A.3).

(A.4).
Trigonometric substitution.

 Substitution Identities , ; , . ; , . ; , .

B. Integration by parts:

C. Integration of rational functions.

(C.1).
Partial fractions

 ; . ; .

(C.2).

(C.3).

(C.4).

Department of Mathematics