What is the integral of ((sin(x))/(sqrt(2-cos(x)))) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((sin(x))/(sqrt(2-cos(x))))

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

2 2 - cos (x) + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Substitute back

u = 2 - cos (x)

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

Apply radical rule:

= 2 2 - cos (x)

Add a constant to the solution

= 2 2 - cos (x) + C

\int (5 - 2 x)^{11} d x

\int (e^{4 t} - t^{- 1}) d t

\int (x^{3} + 2 x + 3) d x

\int \frac{1}{( x + 3 ) ( 9 x ^{2} + 4 )} d x

\int 30 (1 + x^{2}) (7 + 15 x + 5 x^{3})^{10} d x

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