Integration Help: dx/(5-4x-(x^2))^(5/2)

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    Integration
In summary, integration is a mathematical process used to find the area under a curve and is the reverse process of differentiation. Its purpose is to find the cumulative effect of a continuously changing quantity and is used in various fields. The formula for integration is ∫(f(x)dx) and the specific problem for dx/(5-4x-(x^2))^(5/2) is to find the antiderivative of the given function. The technique for solving this problem is to use the substitution method.
  • #1
joseph9496
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Homework Statement



Hi everyone
im stuck with the following integration..

Homework Equations



integral of dx/(5-4x-(x^2))^(5/2)

The Attempt at a Solution



can anyone help me?
thanks
 
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  • #2
… complete the square … !

Hi joseph! :smile:

With quadratics, it's usually best to start by completing the square:

5 - 4x - x^2 = 9 - (x + 2)^2.

(And then you can even change to y = x + 2, dy = dx, if you like!)

Does that help? :smile:
 
  • #3
OH YEAH!
i never thought of that!
thanks alot!
 

What is integration?

Integration is a mathematical process that involves finding the area under a curve, also known as the integral, between two given points on a graph. It is the reverse process of differentiation.

What is the purpose of integration?

The purpose of integration is to find the total or cumulative effect of a continuously changing quantity. It is used in various fields such as physics, engineering, economics, and statistics to solve real-world problems.

What is the formula for integration?

The formula for integration is ∫(f(x)dx), where f(x) represents the function to be integrated and dx represents the differential element. In simpler terms, integration is the process of finding the antiderivative of a function.

What is the specific integration problem for dx/(5-4x-(x^2))^(5/2)?

The specific integration problem for dx/(5-4x-(x^2))^(5/2) is to find the antiderivative of the given function. In other words, we need to find a function whose derivative is equal to dx/(5-4x-(x^2))^(5/2).

What is the technique for solving the given integration problem?

The technique for solving dx/(5-4x-(x^2))^(5/2) is to use the substitution method, where we substitute a variable for the expression inside the parentheses (5-4x-(x^2))^(5/2). This will help us simplify the function and make it easier to find the antiderivative.

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