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

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

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

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

- 2 1 - sin (x) + C

Solution steps

\int \frac{cos ( x )}{1 - sin ( 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 - sin (x)

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

Apply radical rule:

= - 2 1 - sin (x)

Add a constant to the solution

= - 2 1 - sin (x) + C

(e^{3 x})^{^{'}}

x \to 3 lim (\frac{2 x - 3}{x + 5})

\int_{0}^{1} ln (5 x) d x

x \to 0 lim (9 x^{2} + 6 x)

\frac{d}{d x} (\frac{( 2 x ^{2} + 8 x + 4 )}{x})

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