Question

Evaluate using z-substitution $I = \int \frac{1}{2 - \cos x} dx$ A. $\frac{2}{\sqrt{3}} \tan^{-1}(\sqrt{3} \cos \frac{x}{2}) + C$ B. $\frac{2}{\sqrt{3}} \tan^{-1}(\sqrt{3} \tan \frac{x}{2}) + C$ C. None of the options D. $3 \tan^{-1}(\sqrt{3} \tan \frac{x}{2}) + C$ E. $\frac{2}{\sqrt{2}} \tan^{-1}(\sqrt{3} \sin \frac{x}{2}) + C$

          Evaluate using z-substitution
\(I = \int \frac{1}{2 - \cos x} dx\)
A. $\frac{2}{\sqrt{3}} \tan^{-1}(\sqrt{3} \cos \frac{x}{2}) + C$
B. $\frac{2}{\sqrt{3}} \tan^{-1}(\sqrt{3} \tan \frac{x}{2}) + C$
C. None of the options
D. $3 \tan^{-1}(\sqrt{3} \tan \frac{x}{2}) + C$
E. $\frac{2}{\sqrt{2}} \tan^{-1}(\sqrt{3} \sin \frac{x}{2}) + C$

Evaluate using z-substitution
I = ∫(1)/(2 - cos x) dx
A. (2)/(√(3))tan^-1(√(3)cos(x)/(2)) + C
B. (2)/(√(3))tan^-1(√(3)tan(x)/(2)) + C
C. None of the options
D. 3 tan^-1(√(3)tan(x)/(2)) + C
E. (2)/(√(2))tan^-1(√(3)sin(x)/(2)) + C

Added by Monica D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shu Naito

09/01/2024

Step 1

Step 1: Let z = tan(x/2). Show more…

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Evaluate using z-substitution 1 I = cos dx ○ A. ○B. 2-cos z √3 √3 tan¯¹(√3 cos) + C tan¯¹(√3tan) + C OC. None of the options ○ D. 3tan¯¹(√3 tan) + C 2 ○ E. tan¯¹(√3sin) + C