Math Problem Statement
Evaluate the integral. (Use C for the constant of integration.) (sqrtx^2 − 49)/x^4 dx Apply the substitution to transform the integral into a trigonometric integral and evaluate the integral.Show work for each step and complete problem in one chat only
Solution
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Math Problem Analysis
Mathematical Concepts
Integral Calculus
Trigonometric Substitution
Definite and Indefinite Integrals
Formulas
Trigonometric Substitution: x = 7secθ for integrals involving sqrt(x^2 - a^2)
Integral of sec^2(θ): ∫sec^2(θ) dθ = tan(θ) + C
Theorems
Fundamental Theorem of Calculus
Pythagorean Identity: sec^2(θ) - tan^2(θ) = 1
Suitable Grade Level
Undergraduate Calculus Level
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