INTEGRATION METHODS: PARTIAL FRACTIONS APPLICATION EXERCISE

The method of integration by partial fractions is a technique used to integrate rational functions of the form:

∫(P(x)/Q(x)) dx

where P(x) and Q(x) are polynomials.
Steps to integrate by partial fractions
1. *Divide the polynomial P(x) by Q(x)*: obtain the quotient and the remainder.
2. *Decompose Q(x) into factors*: find the linear or quadratic factors.
3. *Write the function as sum of fractions*: assign each factor to a fraction.
4. *Integrate each fraction*: use integration techniques
Advantages
1. Facilitates the integration of rational functions.
2. Allows you to solve complex integrals.
Limitations
1. Only applies to rational functions.
2. Requires decomposition into factors.
Software for integration by partial fractions
1. Mathematica
2. Maple
3. Sympy
4. Wolfram Alpha