Math Problem Statement
integral of square root of 81+x^2 /x
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Integration
Trigonometric Substitution
Formulas
x = 9 tan(θ)
dx = 9 sec^2(θ) dθ
81 + x^2 = 81 sec^2(θ)
∫(1/sin(θ)) dθ = ln |tan(θ/2)| + C
Theorems
Pythagorean Identity: 1 + tan^2(θ) = sec^2(θ)
Trigonometric Substitution
Suitable Grade Level
College Level - Calculus II
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