Integrating 1/(2x^2 + 3x + 1)[(3x^2 - 2x + 1)^(1/2)]

Thread starter Anony111
Start date Feb 27, 2009
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Integrating

In summary, the purpose of integrating the given expression is to find the anti-derivative or original function. This is a fundamental tool used in mathematics and science. To integrate the expression, we can use the substitution method or integration by parts. It can be integrated by hand using various techniques. The applications of integrating this expression can be seen in physics, engineering, and economics. There are special cases and restrictions to consider, such as perfect squares and limits of integration, while integrating this expression.

Feb 27, 2009

Anony111

Homework Statement

integrate

Homework Equations

1/(2x^2 + 3x + 1)[(3x^2 - 2x + 1)^(1/2)]

The Attempt at a Solution

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Feb 27, 2009

tiny-tim

Science Advisor

Homework Helper

have you tried doing it the same way as in your https://www.physicsforums.com/showthread.php?t=295154"?

Last edited by a moderator: Apr 24, 2017

Mar 1, 2009

Anony111

It doesn't work

Mar 1, 2009

cristo

Staff Emeritus

Science Advisor

Anony111 said:

It doesn't work

Why not? Show what you have tried, and then we can help you.

1. What is the purpose of integrating the given expression?

The purpose of integrating the expression 1/(2x^2 + 3x + 1)[(3x^2 - 2x + 1)^(1/2)] is to find the anti-derivative or the original function from which this expression was derived. Integration is a fundamental tool in mathematics and science, used to solve problems involving rates of change, areas, and volumes.

2. How do you approach the integration of this expression?

To integrate this expression, we can use the substitution method, where we substitute a variable for the expression inside the square root. We can also use integration by parts, where we break down the expression into smaller parts and use the product rule for integration.

3. Can this expression be integrated by hand?

Yes, this expression can be integrated by hand. It requires knowledge of integration techniques, such as substitution, integration by parts, and partial fractions.

4. What are the applications of integrating this expression?

Integrating this expression can be applied in various fields, such as physics, engineering, and economics. It can be used to calculate the area under a curve, the volume of a solid, or the displacement of an object with respect to time.

5. Are there any special cases or restrictions for integrating this expression?

One special case for integrating this expression is when the expression inside the square root is a perfect square, in which case the integration becomes simpler. There are also certain restrictions, such as the limits of integration and the constants in the expression, that need to be considered while integrating.