Question

Solve the Antiderivative ​

Answer 1

`√(2) \sin \: x + c`

Explanation:

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