- #1
tmclary
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Homework Statement
Integrate the indefinite integral of 1/((4x^2)+(4x)+5)
Integral Help: 1/((4x^2)+(4x)+5)
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In summary, the conversation is about finding the indefinite integral of 1/((4x^2)+(4x)+5). The first person is asking for help, mentioning that the denominator cannot be factored and has a complex discriminant. The second person suggests completing the square and making a u-substitution to get a tan^-1 type integral. Both parties thank each other for their help.
Integrate the indefinite integral of 1/((4x^2)+(4x)+5)
- #2
Hootenanny
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I assume you mean find the indefinite integral. You also forgot to fill in the following two sections, in particular the final one:tmclary said:
tmclary said:
- #3
tmclary
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Sorry, I have no clue how to get started. The denominator won't factor (at least to linear factors w/ integral coefficients) and the discriminant is complex anyway. So if it's a partial fraction type solution, how do you get started? Thanks.
- #4
Defennder
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Try completing the square of the denominator.
- #5
tmclary
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So 1/(4x^2)+4x+5 =1/((2x+1)^2)+4 and I make a u-sub. Looks like tan^-1 type integral. Correct?
- #6
Hootenanny
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Looks good to metmclary said:
. Choose your substitution carefully.- #7
tmclary
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Thanks for your help, Def & Hoot!
- #8
Hootenanny
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A pleasuretmclary said:
- #9
m_s_a
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http://www.4nw.net/s_thumbnailer-6-2008/hb6z6g1g.JPG
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1. What is the purpose of the integral 1/((4x^2)+(4x)+5)?
The purpose of this integral is to find the area under the curve of the given function represented by 1/((4x^2)+(4x)+5). This area is also known as the definite integral and can be used to solve a variety of problems in mathematics and science.
2. How do you solve the integral 1/((4x^2)+(4x)+5)?
To solve this integral, you can use various methods such as substitution, integration by parts, or partial fraction decomposition. It is important to have a thorough understanding of calculus and its techniques to solve this integral correctly.
3. What is the result of the integral 1/((4x^2)+(4x)+5)?
The result of this integral is a function that represents the area under the curve of 1/((4x^2)+(4x)+5). This function can be evaluated at specific values to find the exact area or used to solve other problems that involve this integral.
4. Can this integral be solved using a calculator or computer program?
Yes, this integral can be solved using a calculator or computer program that has a built-in function for solving integrals. However, it is important to understand the concept and techniques behind solving integrals before relying solely on technology.
5. Are there any real-world applications of this integral?
Yes, this integral has many real-world applications. It can be used to find the volume of irregular shapes, calculate the work done by a varying force, or determine the average value of a function over a given interval. It is also used in fields such as physics, engineering, and economics to solve various problems.
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