SUMMARY
The integral of x^3/(x^2 - 16) can be evaluated using trigonometric substitution, specifically with the substitution x = 4sec(θ). The correct answer is (x^2)/2 + 8 * ln|x^2 - 16| + C, while a common mistake involves an additional -8 in the solution. Both solutions yield the same derivative, confirming their correctness, as the constant can be absorbed into the arbitrary constant C.
PREREQUISITES
- Understanding of trigonometric substitution in integrals
- Familiarity with integration techniques, including integration by parts
- Knowledge of logarithmic properties and their application in calculus
- Ability to differentiate functions to verify solutions
NEXT STEPS
- Study trigonometric substitution methods in calculus
- Learn about integration by parts and its applications
- Explore properties of logarithmic functions in calculus
- Practice differentiating integrals to verify solutions
USEFUL FOR
Students and educators in calculus, particularly those focusing on integration techniques and trigonometric functions.