SUMMARY
The integral of arcsin(x) dx can be solved using integration by parts, resulting in the expression x * arcsin(x) - ∫(x dx)/(√(1-x²)). To evaluate the integral ∫(x dx)/(√(1-x²)), a u-substitution is recommended, specifically using u = 1 - x². This substitution simplifies the integral and facilitates the solution process.
PREREQUISITES
- Integration by parts
- U-substitution method in calculus
- Understanding of arcsine function
- Basic knowledge of square roots and their properties
NEXT STEPS
- Practice integration by parts with different functions
- Explore u-substitution techniques for various integrals
- Study the properties and applications of the arcsine function
- Learn about advanced integration techniques, such as trigonometric substitutions
USEFUL FOR
Students studying calculus, particularly those focusing on integration techniques, as well as educators seeking to enhance their teaching methods for integral calculus.