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

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

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

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

2 2 + sin (x) + C

Solution steps

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

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

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 2 + sin (x)

Add a constant to the solution

= 2 2 + sin (x) + C

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