- #1
Anony111
- 4
- 0
Homework Statement
Please tell me how to integrate this...
Homework Equations
[(2x + 4)][(2x^2 + 3x + 1)^(1/2)]
I'm really having a problem integrating this equation, infact i have no idea
- Thread starter Anony111
- Start date
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- Tags
- Idea Integrating No idea
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SUMMARY
The discussion focuses on the integration of the expression \((2x + 4)\sqrt{2x^2 + 3x + 1}\). The participant successfully factors the quadratic \(2x^2 + 3x + 1\) as \((2x + 1)(x + 1)\) and completes the square to transform the integrand. They utilize the substitution \(u = x + \frac{3}{2}\) and derive a new expression for integration, identifying the need for both substitution and trigonometric methods for solving the integral. A correction is noted regarding the constant term outside the bracket, which should be \(9/8\) instead of \(9/16\).
PREREQUISITES- Understanding of integration techniques, including substitution and trigonometric substitution.
- Familiarity with completing the square for quadratic expressions.
- Knowledge of algebraic manipulation, particularly factoring polynomials.
- Basic calculus concepts, specifically integration of functions involving square roots.
- Study integration techniques using substitution, focusing on complex functions.
- Learn about trigonometric substitution methods for integrals involving square roots.
- Practice completing the square with various quadratic expressions to enhance algebraic skills.
- Explore advanced integration problems to solidify understanding of integration strategies.
Students studying calculus, particularly those tackling integration problems, as well as educators looking for examples of integration techniques and algebraic manipulation.