Question

Which of the following integrals can be integrated using partial fractions using linear factors with real coefficients?

Thank you in advance!

Answer 1

∫ (3x + 1) / (x² + 6x + 8)

Explanation:

The denominator of the first integral factors to:

x⁴ − 1 = (x² − 1) (x² + 1) = (x − 1) (x + 1) (x² + 1)

x² + 1 is not a linear factor, and its roots are not real.

The denominator of the second integral factors to:

x² + 6x + 8 = (x + 2) (x + 4)

These are both linear factors.

The denominator of the third integral is not a linear factor, and its roots are not real.