Indefinite Integrals

Concept: To integrate rational functions, express the integrand using partial fractions and then use standard inverse trigonometric integrals: Step 1: Use partial fractions.
Let:
Step 2: Clear denominators.

Step 3: Compare coefficients.

Step 4: Solve equations.
From (1): Substitute into (2):

Step 5: Rewrite the integral.

Step 6: Use standard formulas.

Step 7: Substitute results.
Rearranging: Conclusion: