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(a) (c) Evaluate √√2 √√2 tan -1 X dx √2x VII) + C +C + √√₂x²2² +2 X √2x tan-¹√23² +2 -1 27127)+4 +C (b) (d) √√√2 8 5 4 √2+1) + C tan X-2 tan √√√2x + √√2x²+2 -1 X +C

(a) (c) Evaluate √√2 √√2 tan -1 X dx √2x VII) + C +C + √√₂x²2² +2 X √2x tan-¹√23² +2 -1 27127)+4 +C (b) (d) √√√2 8 5 4 √2+1) + C tan X-2 tan √√√2x + √√2x²+2 -1 X +C

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 3** Evaluate \(\int \frac{1}{(x^2 + 2)^2} \, dx\). **Options:** (a) \(\frac{\sqrt{2}}{8} \left( \tan^{-1} \frac{x}{\sqrt{2}} + \frac{\sqrt{2}x}{x^2 + 2} \right) + C\) (b) \(\frac{\sqrt{2}}{8} \left( \tan x - \frac{\sqrt{2}x}{x^2 + 2} \right) + C\) (c) \(\frac{\sqrt{2}}{8} \left( \tan^{-1} \frac{x}{\sqrt{2}} - \frac{\sqrt{2}x}{x^2 + 2} \right) + C\) (d) \(\frac{\sqrt{2}}{4} \left( \tan^{-1} \frac{x}{\sqrt{2}} + \frac{\sqrt{2}x}{x^2 + 2} \right) + C\) **Explanation** The problem presents an integral that requires evaluation, with four potential solutions provided as options. Each option involves the inverse tangent function, adjustments within the expression, and includes a constant of integration \(C\).
Transcribed Image Text:**Problem 3** Evaluate \(\int \frac{1}{(x^2 + 2)^2} \, dx\). **Options:** (a) \(\frac{\sqrt{2}}{8} \left( \tan^{-1} \frac{x}{\sqrt{2}} + \frac{\sqrt{2}x}{x^2 + 2} \right) + C\) (b) \(\frac{\sqrt{2}}{8} \left( \tan x - \frac{\sqrt{2}x}{x^2 + 2} \right) + C\) (c) \(\frac{\sqrt{2}}{8} \left( \tan^{-1} \frac{x}{\sqrt{2}} - \frac{\sqrt{2}x}{x^2 + 2} \right) + C\) (d) \(\frac{\sqrt{2}}{4} \left( \tan^{-1} \frac{x}{\sqrt{2}} + \frac{\sqrt{2}x}{x^2 + 2} \right) + C\) **Explanation** The problem presents an integral that requires evaluation, with four potential solutions provided as options. Each option involves the inverse tangent function, adjustments within the expression, and includes a constant of integration \(C\).
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