Question

What is the strategy for integrating the fraction (Ax + B)/(γx² + r) to make it suitable for standard sub, reverse power rule, and log integrals?

a) Split it into two fractions
b) Take out constants from the numerators
c) Convert it into a logarithmic form
d) Use the reverse power rule directly

Answer 1

The strategy for integrating the fraction (Ax + B)/(γx² + r) involves splitting it into two fractions, taking out constants from the numerators, converting it into logarithmic form, and using the reverse power rule directly.

Step-by-step explanation:

The strategy for integrating the fraction (Ax + B)/(γx² + r) to make it suitable for standard sub, reverse power rule, and log integrals involves the following steps:

1. Split the fraction into two fractions. To do this, express the numerator as the sum of two terms, Ax and B.
2. Take out the constants from the numerators. This means factoring out A from Ax and B from B.
3. Convert the fraction into logarithmic form. This can be done by rewriting the expression as (1/γ)ln(γx² + r).
4. Use the reverse power rule directly. This means recognizing that the original fraction can be integrated directly using the reverse power rule without any additional steps.