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

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

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

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

- 2 1 + cos (x) + C

Solution steps

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

Apply u-substitution

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

= \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}}

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

Substitute back

u = 1 + cos (x)

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

Apply radical rule:

= - 2 1 + cos (x)

Add a constant to the solution

= - 2 1 + cos (x) + C

f (x) = (x + 2) \cdot (2 \cdot x^{2} - 2)

\int - 3 sec (x) tan (x) - 3 csc (x) cot (x) d x

\int \frac{1}{6 x} d x

(t - sin (t))^{^{'}}

\frac{d}{d x} (lo g_{2} (x^{2}))

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