Question

Integration by partial fractions calculator with steps.

A) Online integral calculators provide step-by-step solutions.
B) Integration by partial fractions is not a step-by-step process.
C) Solve the system of equations formed by the partial fractions.
D) Use the substitution method to find the partial fractions.

Answer 1

Integration by partial fractions is a technique used to integrate a rational function by decomposing it into simpler fractions. The process involves solving a system of equations formed by the partial fractions.

Step-by-step explanation:

Integration by partial fractions is a technique used to integrate a rational function by decomposing it into simpler fractions. The process involves solving a system of equations formed by the partial fractions. Here are the steps to integrate a rational function using partial fractions:

1. Factor the denominator of the rational function into irreducible factors.
2. Write the given rational function as the sum of partial fractions, where each partial fraction has a denominator corresponding to one of the irreducible factors.
3. Write a system of equations by equating the numerators of the partial fractions to the corresponding terms obtained from the original rational function.
4. Solve the system of equations to find the unknown coefficients in the partial fractions.
5. Combine the partial fractions and integrate each term separately using the power rule or other integration techniques.