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

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

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

2 sin (x) + C

Solution steps

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

\frac{cos ( x )}{2 sin ( x )} = \frac{1}{2} \frac{cos ( x )}{sin ( x )}

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

Take the constant out:

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

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

Apply u-substitution

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

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

Simplify

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

= 2 sin (x)

Add a constant to the solution

= 2 sin (x) + C

x \to 0 lim ((\frac{1}{5 x}) - (\frac{1}{e ^{5 x}} - 1))

3 (5^{x})

\int_{0}^{2} (2 x - 5)^{2} d x

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

y^{^{'}} = \frac{3 x ^{4} + y ^{4}}{x y ^{3}}

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