SUMMARY
The integral of Sqrt(2x + 7) dx can be solved using the substitution method. By letting u = 2x + 7, the differential du becomes 2dx, allowing for the integral to be rewritten as (1/2) ∫ u^(1/2) du. This results in the final solution of (1/3)(2x + 7)^(3/2) + C. Verification through differentiation confirms the application of the chain rule.
PREREQUISITES
- Understanding of integral calculus
- Familiarity with substitution methods in integration
- Knowledge of the chain rule in differentiation
- Basic algebraic manipulation skills
NEXT STEPS
- Study the method of integration by substitution in detail
- Learn about the chain rule in differentiation
- Practice solving integrals involving square roots
- Explore advanced integration techniques such as integration by parts
USEFUL FOR
Students studying calculus, mathematics educators, and anyone seeking to improve their integration skills.