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evaluate ∫ (cos^2(x) – sin^2(x)) / sqrt(1 + cos 4x) dx

evaluate
∫ (cos^2(x) – sin^2(x)) / sqrt(1 + cos 4x) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{cos^{2}x-sin^{2}x}{\sqrt{1+cos4x}}dx
I = \int \frac{cos^{2}x-sin^{2}x}{\sqrt{2cos^{2}2x}}dx
I = \frac{1}{\sqrt{2}}\int \frac{cos^{2}x-sin^{2}x}{cos2x}dx
I = \frac{1}{\sqrt{2}}\int \frac{cos2x}{cos2x}dx
I = \frac{1}{\sqrt{2}}\int dx
I = \frac{x}{\sqrt{2}} + c

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