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

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

Popular >

integral of (sin(x))/(sqrt(1+2cos(x)))

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

- 1 + 2 cos (x) + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{1 + 2 u} d u

= \int - \frac{1}{1 + 2 u} d u

Take the constant out:

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

= - \int \frac{1}{1 + 2 u} d u

Apply u-substitution

: \int 1 d v

= - \int 1 d v

Integral of a constant:

\int a d x = a x

= - 1 \cdot v

Substitute back

= - 1 \cdot 1 + 2 cos (x)

Simplify

= - 1 + 2 cos (x)

Add a constant to the solution

= - 1 + 2 cos (x) + C

\int \frac{2 x - 3}{x ^{2} + x + 5} d x

\int \frac{cos ( ln ( 4 x ) )}{5 x} d x

\int x^{\frac{1}{3}} ln (x) d x

\int tan (\frac{1}{4} x) d x

\int e^{c o s (z)} sin (z) d z

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