Integration of rational functions by division and partial fractions

The  exercise appears under the Integral calculus Math Mission. This exercise uses partial fraction decomposition to find the integral of rational functions.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the indefinite integral: This problem asks for the integral of a rational function. The student is expected to split the rational function by partial fractions and then find the integral of the separate parts using properties of integrals.Ibpfd1.png

Strategies
Knowledge of u-substitution and partial fraction decomposition are encouraged to ensure success on this exercise.
 * 1) Partial fraction decomposition is the process by which fractions can be split.
 * 2) The common integrals needed (after splitting) are logarithms, inverse tangent, and occasionally power rules with negative exponents.
 * 3) Since the integrals on this problem are indefinite, one can determine the correct answer by differentiating the answer choices and finding which one simplifies to the required integrand.

Real-life Applications

 * 1) Integral techniques are important for finding any integral that is not immediately set up as one that is recognizable.
 * 2) Integration has many applications in the sciences and economics to find "totals."