Math Problem Statement
3dx /(x(x2 + 4)2)
Solution
The given expression is:
We are tasked with finding the indefinite integral of this function.
Step-by-step Solution:
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Substitute , which implies . So, .
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The integral becomes:
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The integral of is .
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Substituting back , we get:
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Therefore, the indefinite integral is: where is the constant of integration.
Would you like more details on any specific part of this solution?
Related Questions:
- How would you approach a similar integral with a different denominator, say ?
- What changes if the power of was different, like 3 or higher?
- Can we solve this integral using partial fractions?
- How can we compute the definite integral of this expression over a specific range?
- What is the geometric interpretation of the integral ?
Tip:
When solving integrals with quadratic terms, trigonometric substitution often simplifies the process, especially when the quadratic expression resembles a trigonometric identity like .
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Math Problem Analysis
Mathematical Concepts
Integration
Substitution Method
Indefinite Integrals
Formulas
Integral of 1/u^n is -1/(n-1) * u^(n-1) for n ≠ 1
Substitution: u = x^2 + 4, du = 2x dx
Theorems
Substitution Rule for Integration
Suitable Grade Level
Undergraduate Calculus