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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Take the constant out:

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

= - \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}})

Simplify

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

= 2 1 - sin (x)

Add a constant to the solution

= 2 1 - sin (x) + C

\int \frac{x ^{\frac{3}{2}}}{3} d x

\int \frac{7 x ^{3} - 7 x + 4}{x ^{3} - x ^{2}} d x

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

\int sinh (y) d y

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