What is the integral of (sin(x))/(sqrt(cos(x)+1)) ?

The integral of (sin(x))/(sqrt(cos(x)+1)) is -2sqrt(cos(x)+1)+C

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integral of (sin(x))/(sqrt(cos(x)+1))

\int \frac{sin ( x )}{cos ( x ) + 1} d x

- 2 cos (x) + 1 + C

Solution steps

\int \frac{sin ( x )}{cos ( x ) + 1} d x

Apply u-substitution

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

Take the constant out:

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

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

Apply the Power Rule

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

Substitute back

u = cos (x) + 1

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

Apply radical rule:

= - 2 cos (x) + 1

Add a constant to the solution

= - 2 cos (x) + 1 + C

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