SUMMARY
The integral ∫ (x-5)/√(x-6) dx can be solved using u-substitution by letting u = x - 6, which simplifies the expression. The differential du equals dx, and substituting x with u + 6 transforms the integral into ∫ (u + 1)/√u du. This can be further simplified to ∫ (u^(1/2) + u^(-1/2)) du. The integrals of u^(1/2) and u^(-1/2) are straightforward, yielding (2/3)u^(3/2) and 2u^(1/2) respectively, leading to the final solution.
PREREQUISITES
- Understanding of u-substitution in integral calculus
- Familiarity with basic integral rules and techniques
- Knowledge of manipulating algebraic expressions
- Ability to differentiate between different forms of integrals
NEXT STEPS
- Practice solving integrals using u-substitution with varying functions
- Explore advanced integration techniques such as integration by parts
- Learn about definite integrals and their applications
- Study the properties of square roots in integrals for better simplification
USEFUL FOR
Students studying calculus, particularly those focusing on integration techniques, as well as educators looking for examples of u-substitution in action.