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

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

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

2 sin (x) + 1 + C

Solution steps

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

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

Apply radical rule:

= 2 sin (x) + 1

Add a constant to the solution

= 2 sin (x) + 1 + C

\int sec^{3} (p) tan (p) d p

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

\int 1080 e^{- 0.9 x} d x

\int \frac{5 x - 5}{3 x ^{2} - 8 x - 3} d x

\int cos (2 sin (x)) cos (x) d x

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