What is the integral of 1/(5+3cos(x)) ?

The integral of 1/(5+3cos(x)) is 1/2 arctan((tan(x/2))/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(5+3cos(x))

\int \frac{1}{5 + 3 cos ( x )} d x

\frac{1}{2} arctan (\frac{tan ( \frac{x}{2} )}{2}) + C

Solution steps

\int \frac{1}{5 + 3 cos ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{2} + 4} d u

= \int \frac{1}{u ^{2} + 4} d u

Apply Integral Substitution

= \int \frac{1}{2 ( v ^{2} + 1 )} d v

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{v ^{2} + 1} d v = arctan (v)

= \frac{1}{2} arctan (v)

Substitute back

= \frac{1}{2} arctan (\frac{tan ( \frac{x}{2} )}{2})

Add a constant to the solution

= \frac{1}{2} arctan (\frac{tan ( \frac{x}{2} )}{2}) + C

\frac{d}{d x} (ln cos (\frac{π}{x}))

\int_{0}^{4} 5 d x

\int \frac{x ^{3}}{x ^{2} - 1} d x

25 - x^{2} d x

\frac{\partial}{\partial y} (x e^{2 yz})

What is the integral of 1/(5+3cos(x)) ?
The integral of 1/(5+3cos(x)) is 1/2 arctan((tan(x/2))/2)+C