What is the integral of (1-cos(2x))^{1/2} ?

The integral of (1-cos(2x))^{1/2} is -2^{1/2}cos(x)+C

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integral of (1-cos(2x))^{1/2}

\int (1 - cos (2 x))^{\frac{1}{2}} d x

- 2^{\frac{1}{2}} cos (x) + C

Solution steps

\int (1 - cos (2 x))^{\frac{1}{2}} d x

Simplify

(1 - cos (2 x))^{\frac{1}{2}} : 2^{\frac{1}{2}} sin (x)

= \int 2^{\frac{1}{2}} sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2^{\frac{1}{2}} \cdot \int sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= 2^{\frac{1}{2}} (- cos (x))

Simplify

= - 2^{\frac{1}{2}} cos (x)

Add a constant to the solution

= - 2^{\frac{1}{2}} cos (x) + C

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What is the integral of (1-cos(2x))^{1/2} ?
The integral of (1-cos(2x))^{1/2} is -2^{1/2}cos(x)+C