Math Problem Statement
what is the f(x) if the first derivative of f(x) is x / (9 - x^4)
Solution
Given that the first derivative of is:
To find , we need to integrate with respect to .
Step 1: Set up the integral
Step 2: Simplify the integral
We notice that the denominator involves , and the numerator is . A substitution may help simplify the integral.
Let: Then, the derivative of with respect to is: To match the term in the numerator, we need to isolate a single , so rewrite as: [ f(x) = \int \frac{1}{9 - x^4} dx
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Integration
Substitution Method
Formulas
f'(x) = x / (9 - x^4)
Integration formula: ∫ f'(x) dx = f(x)
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Grades 11-12 (Advanced Calculus)