What is the integral of (-cos(3x))/(sqrt(1-sin(3x))) ?

The integral of (-cos(3x))/(sqrt(1-sin(3x))) is 2/3 sqrt(1-sin(3x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (-cos(3x))/(sqrt(1-sin(3x)))

\int \frac{- cos ( 3 x )}{1 - sin ( 3 x )} d x

\frac{2}{3} 1 - sin (3 x) + C

Solution steps

\int \frac{- cos ( 3 x )}{1 - sin ( 3 x )} d x

Take the constant out:

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

= - \int \frac{cos ( 3 x )}{1 - sin ( 3 x )} d x

Apply u-substitution

: \int \frac{cos ( u )}{3 1 - sin ( u )} d u

= - \int \frac{cos ( u )}{3 1 - sin ( u )} d u

Take the constant out:

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

= - \frac{1}{3} \cdot \int \frac{cos ( u )}{1 - sin ( u )} d u

Apply u-substitution

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

= - \frac{1}{3} \cdot \int - \frac{1}{v} d v

Take the constant out:

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

= - \frac{1}{3} (- \int \frac{1}{v} d v)

Apply the Power Rule

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

= - \frac{1}{3} (- 2 v^{\frac{1}{2}})

Substitute back

= - \frac{1}{3} (- 2 (1 - sin (3 x))^{\frac{1}{2}})

Simplify

- \frac{1}{3} (- 2 (1 - sin (3 x))^{\frac{1}{2}}) : \frac{2}{3} 1 - sin (3 x)

= \frac{2}{3} 1 - sin (3 x)

Add a constant to the solution

= \frac{2}{3} 1 - sin (3 x) + C

\int \frac{1}{cos ^{2} ( x ) + 4 sin ^{2} ( x )} d x

\int - \frac{1}{4 x ^{2}} d x

\int \frac{1 + 2 e ^{x}}{e ^{2 x}} d x

\int \frac{2}{x ^{2} + 2 x + 5} d x

\int x^{2} (x^{3} - 2)^{\frac{1}{7}} d x

What is the integral of (-cos(3x))/(sqrt(1-sin(3x))) ?
The integral of (-cos(3x))/(sqrt(1-sin(3x))) is 2/3 sqrt(1-sin(3x))+C