Question

Solve the Antiderivative ​

Answer 1

Answer:

$\sqrt{2} \sin \: x + c$

Step-by-step explanation:

$\int \sqrt{1 + \cos(2x)} \: \: dx \\ \\ = \int \sqrt{1 + 2\cos ^{2}x - 1 } \: \: dx \\ \\ = \int \sqrt{ 2\cos ^{2}x } \: \: dx \\ \\ = \int \sqrt{ 2 }\cos x \: \: dx \\ \\ = \sqrt{ 2 }\int \cos x \: \: dx \\ \\ = \sqrt{2} \sin \: x + c$