What is the integral of sqrt(1-sin(u)) ?

The integral of sqrt(1-sin(u)) is 2sqrt(sin(u)+1)+C

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integral of sqrt(1-sin(u))

\int 1 - sin (u) d u

2 sin (u) + 1 + C

Solution steps

\int 1 - sin (u) d u

Apply u-substitution

: \int \frac{1}{v + 1} d v

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

Apply u-substitution

: \int \frac{1}{w} d w

= \int \frac{1}{w} d w

Simplify

\frac{1}{w} : \frac{1}{w}

= \int \frac{1}{w} d w

Simplify

= \int \frac{1}{w} d w

Apply the Power Rule

: 2 w^{\frac{1}{2}}

= 2 w^{\frac{1}{2}}

Substitute back

= 2 (sin (u) + 1)^{\frac{1}{2}}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 sin (u) + 1

Add a constant to the solution

= 2 sin (u) + 1 + C

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What is the integral of sqrt(1-sin(u)) ?
The integral of sqrt(1-sin(u)) is 2sqrt(sin(u)+1)+C