Math Problem Statement

\int _0^{1:}\frac{1}{x^2-9}:dx

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Definite Integrals
Partial Fraction Decomposition
Logarithms

Formulas

Partial fraction decomposition: \frac{1}{x^2 - 9} = \frac{1/6}{x - 3} - \frac{1/6}{x + 3}
Integral of \frac{1}{x - a}: \int \frac{1}{x - a} dx = \ln |x - a|
Logarithmic properties: \ln \left(\frac{a}{b}\right) = \ln a - \ln b

Theorems

Properties of Definite Integrals
Logarithmic Integration Theorem
Partial Fraction Decomposition

Suitable Grade Level

Undergraduate Calculus