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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sqrt(tan(x)))/(sin(2x))

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

tan (x) + C

Solution steps

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

Apply u-substitution

: \int \frac{tan ( \frac{u}{2} )}{2 sin ( u )} d u

= \int \frac{tan ( \frac{u}{2} )}{2 sin ( u )} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{tan ( \frac{u}{2} )}{sin ( u )} d u

Apply u-substitution

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

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

Apply the Power Rule

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

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

Substitute back

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

Simplify

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

= tan (x)

Add a constant to the solution

= tan (x) + C

\frac{d}{d x} (2 x^{3 x})

\frac{\partial}{\partial x} (\frac{1}{2} (x - y)^{2})

t y^{^{'}} + 2 y = 4 t^{2}

x \to - 2 lim (\frac{x}{x ^{2} - 4})

\frac{d}{d x} (2 sin^{3} (x) - 3 cos^{2} (x))

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