Find the area below the graph of f, but f is in fractional form?

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Homework Help Overview

The problem involves finding the area under the graph of a fractional function defined as f(x) = (2x + 5)/[(x + 2)²(x + 3)²] over the interval [0, 1]. The original poster expresses difficulty in evaluating integrals of this form and seeks assistance in finding the antiderivative.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how to evaluate the definite integral and questions how to find the antiderivative of the given function. Some participants suggest the use of partial fractions as a potential method to approach the problem.

Discussion Status

The discussion has progressed with participants offering suggestions, such as the use of partial fractions. The original poster later indicates they found a helpful resource that provided guidance on a similar question, suggesting a productive direction has been achieved.

Contextual Notes

The original poster mentions that they have not learned how to use partial fractions, indicating a gap in their knowledge that may affect their ability to solve the problem independently.

LilTaru
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Homework Statement



Find the area below the graph of f.

f(x) = (2x + 5)/[(x + 2)2(x + 3)2] xE [0, 1]

Homework Equations



I know the area under the graph is the definite integral with upper limit = 1; lower limit = 0.

The Attempt at a Solution



I have such a hard time evaluating integrals when they are in fractional form. I know if G(x) is the antiderivative of f, then:

Area = G(1) - G(0)

But, I don't know how to find an antiderivative for f? It seems impossible to me! Someone please help!
 
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Have you tried partial fractions? They're going to be very useful here.
 
We never learned how to use them... Is there a website that shows how to use them?
 
Nevermind... Found a website with a similar question and a step-by-step guide of how to solve it and why! It was really helpful! Thanks for putting me on the right track!
 
It was no problem. Have a great day!
 

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