Question

Integration of rational functions by partial fractions calculator.

A) Euler's Method Calculator
B) Runge-Kutta Method Calculator
C) Simpson's Rule Calculator
D) Partial Fraction Decomposition Calculator

Answer 1

Integration of rational functions by partial fractions is a technique used in calculus to integrate rational functions. This technique involves factoring the denominator of the rational function and writing it as the sum of partial fractions with unknown numerators. The unknown numerators are then determined by equating coefficients of like terms and the partial fractions are integrated using the power rule for integration.

Step-by-step explanation:

Integration of rational functions by partial fractions is a technique used in calculus to integrate rational functions. When a rational function cannot be directly integrated, it is decomposed into partial fractions, which are simpler fractions that can be integrated easily. This technique is particularly useful when the degree of the numerator is greater than or equal to the degree of the denominator.

To decompose a rational function into partial fractions, follow these steps:

1. Factor the denominator of the rational function.
2. Write the rational function as the sum of partial fractions with unknown numerators.
3. Find the unknown numerators by equating the coefficients of like terms on both sides of the equation.
4. Integrate each of the partial fractions by using the power rule for integration.
5. If necessary, simplify the result by combining like terms or using algebraic techniques.