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

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

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

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

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

Solution steps

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

Apply u-substitution

= \int - \frac{1}{u + 1} d u

Take the constant out:

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

= - \int \frac{1}{u + 1} d u

Apply u-substitution

= - \int \frac{1}{v} d v

Simplify

\frac{1}{v} : \frac{1}{v}

= - \int \frac{1}{v} d v

Simplify

= - \int \frac{1}{v} d v

Apply the Power Rule

= - 2 v^{\frac{1}{2}}

Substitute back

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

Add a constant to the solution

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

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