Question

Integration by partial fractions calculator.

A) Use the power rule for integration.
B) Integration by partial fractions is not a valid method.
C) Separate the fraction into simpler fractions and integrate each part.
D) Use the substitution method for integration.

Answer 1

Integration by partial fractions is a valid method used to integrate a rational function. It involves breaking down the fraction into simpler fractions and integrating each part separately.

Step-by-step explanation:

The correct answer is C) Separate the fraction into simpler fractions and integrate each part.

Integration by partial fractions is a valid method used to integrate a rational function, which is a fraction where the numerator and denominator are polynomials. The method involves breaking down the rational function into simpler fractions and then integrating each part separately.

Here is a step-by-step explanation:

1. Factorize the denominator of the rational function into linear and irreducible quadratic factors.
2. Express the rational function as the sum of partial fractions, with each fraction having a denominator corresponding to the factors obtained in step 1.
3. Integrate each partial fraction separately using the power rule for integration.

By integrating each part separately, you can evaluate the integral of the original rational function.