SUMMARY
The integral of (2)/(x^2 + 1) results in 2tan-1(x) + C, as confirmed by multiple users in the discussion. The confusion arose from the integration of (2x)/(x^2 + 1), which leads to ln(x^2 + 1) + C. Users referenced Wolfram Alpha for verification, which provided consistent results for both integrals. The discussion highlights the importance of recognizing the role of the numerator in determining the integration technique.
PREREQUISITES
- Understanding of basic calculus concepts, specifically integration.
- Familiarity with logarithmic and inverse trigonometric functions.
- Knowledge of the properties of derivatives, particularly d/dx(tan-1(x)).
- Experience using computational tools like Wolfram Alpha for verification of mathematical solutions.
NEXT STEPS
- Study integration techniques involving rational functions.
- Learn about the properties and applications of inverse trigonometric functions.
- Explore the use of Wolfram Alpha for solving calculus problems.
- Practice integrating various forms of functions to solidify understanding of integration rules.
USEFUL FOR
Students studying calculus, mathematics educators, and anyone seeking to improve their skills in integration techniques and verification methods using computational tools.