Question

What are the three methods for partial fraction decomposition?

A) Polynomial division, u-substitution, and expected expression
B) Polynomial division, my 'u' method, and expected expression
C) Polynomial division, integration by parts, and my 'u' method
D) Polynomial division, u-substitution, and integration by parts

Answer 1

The three methods for partial fraction decomposition are polynomial division, u-substitution, and integration by parts, option D.

Step-by-step explanation:

The correct answer is D) Polynomial division, u-substitution, and integration by parts.

In partial fraction decomposition, we break down a rational function into simpler fractions. The three methods mentioned offer different ways to achieve this decomposition.

Polynomial division is used to divide the numerator into the denominator to obtain polynomial factors. U-substitution involves substituting a variable 'u' for a polynomial factor to simplify the integration. And integration by parts applies the formula ∫u dv = uv - ∫v du to integrate a product of functions.